eChapters

Evapotranspiration (ET) is the combined loss of water from vegetation and soil. When water is not a limiting factor at a site, the rate of ET is primarily controlled by meteorological factors like solar radiation, temperature, wind and relative humidity. The measurement of ET under natural conditions is of great importance in the water resource management and irrigation planning. Potential evapo-transpiration (PET) is the evaporation from a surface if water was never a limiting factor. PE-can also be calculated using empirical formulae.

It is the actual minimum temperature experienced by the plants near ground surface. The grass minimum temperature is lower than the air temperature at 4 ft level. It is the temperature recorded in open air ground on short turf, with the bulb of the thermometer just in contact with the tips of the blades of grass. It is also described as the temperature at 5.0 cm (2 inches) above ground. It is used during October to March period only when frost occurrence is expected. The readings of the grass minimum thermometer indicate the possibility of ground frosts, which is important information for farmers, gardeners and growers.

Aim

To measure horizontal distance on the level ground using chain

Materials required

Chain

Ranging rods

Chain pins

Field note book

The presence of moisture in atmosphere is termed as humidity and plays an important role in formation of weather system and plant as well as insect-pest growth and development. An abundance of moisture results in a rich natural flora and makes possible a wide choice of crops. Deficiency of moisture, on the other hand, permits only narrow range of crops. Humidity also affects the water requirement and the rate of transpiration. Reduction in transpiration reduces the translocation of food material and uptake of nutrients. High humidity with high temperature favours the outbreak of pest and disease. Moisture stress condition reduces the cell size and shape and ultimately plant growth and yield is reduced. High soil moisture and humidity condition cause failure in establishing stand of legumes and pulses. Excess of soil moisture in earlier growing season may result in more vegetative growth and delayed flowering.

Aim

To measure irrigation water by area-velocity method by using (i) float and (ii) current meter

Apparatus required

Float

Current meter

Theory

The rate of flow of water in open channel can be determined by multiplying the cross sectional area of the flow section at right angles to the direction of flow by the average velocity of water. In area-velocity method, the water can be measured at motion. The water is measured in motion by means of rate of flow or discharge and is expressed in litre per second (lps), litre per minute (lpm), cubic metre per second (m³/s), etc. Litre per second: A continuous flow amounting to 1 litre passing through a point each second. Cubic metre per second: A flow of water equivalent to a stream of 1 m long, 1 m wide and 1 m deep flowing at a velocity of 1 metre per second. In area-velocity method, the velocity of water is measured either by float or current-meter

Aim

To measure the irrigation water by using parshall flume

Construction of Parshall flume

Parshall flume is a water measuring device that can be used to measure water flowing in an open channel and intended primarily for use in irrigation. The flume consists of a converging inlet section, a throat section with straight parallel sides, and a diverging outlet section (Fig.61.1). The floor of the converging section is level with walls which converge in the direction of flow, towards the throat. The throat section constitutes the middle portion of the Parshall flume. The floor of the throat section is dips downward in the direction of flow, but the walls are parallel. The throat width specifies the dimensions of the parshall flume. The diverging outlet section of the flume has a floor which rises in the direction of flow. The walls become further separated in the direction of flow (diverge).The parshall flume can be constructed by G.I. sheet, aluminum sheet, M.S. sheet, brick masonry, reinforced concrete or timber. Flumes made of G.I. or aluminum sheets are easily portable. Brick masonry and concrete flumes are permanently constructed in the channels. Stilling wells should be constructed at the side to take measurements.

Aim

To measure the irrigation water by using orifice

Orifices

An orifice is an opening in a bulk head with closed perimeter usually circular or rectangular cross-section through which water flows. For measurement of water, orifices are fabricated by making an accurate cut of proper size and shape in a mild steel sheet, aluminum plate etc. Proper machining is done to have a sharp edge through which water flows (Fig.60.1).

Free discharge

If the downstream water level is lower than the bottom of the orifice opening, the water jet discharges freely into the air and then it is said to be free discharge. The depth of water on the upstream side of the orifice that causes the flow is called the head. The orifice flow formulae can be applied only when the orifice flows fully.

Aim

To measure the irrigation water by using weirs

a) Weirs

A weir is a notch or opening of some definite shape installed on a channel or a stream through which waterfalls (Fig.59.1). Materials like wood, concrete, mild steel, rigid PVC etc. can be used for construction of a weir. Mainly a cut on a sheet metal is used for fabrication of weirs, to be installed at various locations in a channel. Advantages of weirs are (i) capable of accurately measuring a wide range of flows (ii) easy to construct, portable and adjustable (iii) tends to provide more accurate discharge rating than flumes and orifices.

Aim

To measure irrigation water by volumetric method

Apparatus required

Siphon tube

Stop watch

Measuring bucket

Aim

To measure the irrigation water flowing through a pipe by using Venturimeter

Theory

A venturimeter is a device used to measure the rate of flow of a fluid through a pipe and is often fixed permanently at different sections of the pipeline to know the discharge there. Venturimeter consists of three parts: (i) a short converging part (ii) a throat (iii) a diverging part (Fig.62.1). In the venturimeter, the fluid is accelerated through a converging cone of angle 15-20° and the pressure difference between the upstream side of the cone and the throat is measured, and provides the signal for the rate of flow. Due to the constriction there is an increase in the flow velocity and hence an increase in the kinetic energy. The fluid slows down in a cone with smaller angle (5-7°) where most of the kinetic energy is converted back to pressure energy. Because of the cone and the gradual reduction in the area there is no “vena contracta”. The flow area is at minimum at the throat.

Measurement of water used in irrigation ensures the application of required amount of water in crops. Knowing the rate of flow the adjustment to period of control at gates, etc. can be done to regulate the water at different branches of canals. To get the total control over the supply of water there should have the provision of water measurement at the critical points in irrigation systems.

Units of Measurement

Water is measured at rest or in motion. The water of reservoir, ponds, tanks, etc. at rest is measured in volumetric unit as liter, cubic meter, hectare-meter and hectare-centimeter. Water flowing in rivers, canals, channel, etc. is measured in liter/s, liter per hour, meter per second and hectare-meter per hour or day.

Measurement of water used in irrigation ensures the application of required amount of water in crops. Knowing the rate of flow the adjustment to period of control at gates, etc. can be done to regulate the water at different branches of canals. To get the total control over the supply of water there should have the provision of water measurement at the critical points in irrigation systems.

Units of Measurement

Water is measured at rest or in motion. The water of reservoir, ponds, tanks, etc. at rest is measured in volumetric unit as liter, cubic meter, hectare-meter and hectare-centimeter. Water flowing in rivers, canals, channel, etc. is measured in litre/sec , liter per hour, meter per sec and hectare-meter per hour or day.

Water Quantity and Measurement: The amount of water to be applied and its measurement are crucial aspects of irrigation management. There are various methods and tools used to measure and control the flow of water, including:
1. Parshall flume
2. Orifice
3. Weirs
4. Water meter
5. Float method
6. V-Notch
Methods of Soil Moisture Measurement
The measurement of soil moisture is essential to determine when to irrigate, the amount of water needed, to evaluate evapotranspiration, and to monitor soil matric potential. Soil moisture is measured in two ways: direct and indirect methods.
Direct Methods
1. Gravimetric method: The gravimetric method is a standard method for measuring soil water content directly. It involves collecting soil samples from the field and determining their moist and dry weights. The mass water content is then calculated as the ratio of the weight loss in drying to the dry weight of the soil sample. This method is accurate but time-consuming and requires laboratory equipment.
2. Spirit burning method: The spirit burning method is a direct method for measuring soil moisture in the field. Soil moisture is evaporated by adding alcohol and igniting it. The time taken for the soil to dry is then used to calculate the soil moisture content. This method is quick and easy but can be affected by soil temperature and organic matter content.

Object: Measurement of leaf area by graph paper method.

Material required: leaves, graph paper and pencil or pen.

Leaf area is an important attribute in bio-productivity studies, as it bears an important and direct relationship to photosynthesis and transpiration. Leaf area is also important in determining the percentage of solar radiation intercepted by an individual plant or crop canopy. Photosynthesis centers on individual leaf. However, productivity depends not only on individual leaves but on stand of vegetation and canopy structure. The photosynthetic productivity of a canopy depends on both the amount of leaves present and the configuration of the leaves making up the canopy. Thus, leaf area has direct bearing on plant growth and final yield.

Aim: To know the actual length of a Thomas splint & measurement for an animal.

Procedure

Animal is kept in lateral recumbancy with affected limb upward.

After padding & medical bending of Thomas splint, it is fitted upon the fractured limb.

At the time of measurement, the limb should be kept vertical to body for accurate measurement, otherwise the length of Thomas splint may be shorteror longer if the limb is kept forward or backward respectively.

The ring of the Thomas splint is kept close to the axilla (forelimb), groin (hind limb).

Limb is put downward & Thomas splint is pushed upward keeping both the extension bamboo of Thomas splint in crossed manner, measurement of length of Thomas splint is taken up to the bulb of the heel & mark is recorded.

The excess length is trimmed short (figure-1). Two nicks are made on the distal end for retaining the thread in position.

Both the distal ends are tied together with thread, soft padding is placed at the site where hoof is to be kept & retained in position with bandage (figure-3).

Introduction

The major biogenic gases, which contribute to global warming, are carbon dioxide, methane and nitrous oxide. Out of these, methane is the most important gas because its thermal absorption is 30 times greater than carbon dioxide, though its atmospheric concentration is about 200 times less than carbon dioxide. Atmospheric measurements of greenhouse gases indicate that methane concentration had increased by 1 per cent annually to 1.7 ppm (by volume) during the last decade. The steady increase of atmospheric methane concentration in the past 200 years has attracted much attention.

Flooded rice soils provide an optimum environment for methane production and emission. Flooding a soil creates essential redox potential, anaerobic decomposition of organic matter and stabilizes the soil pH near neutral, thus makes the congenial environment for methane emission.

Rice is the world’s most important food crop

Introduction

The soil microbial biomass is an important component of the soil organic matter that regulates the transformation and storage of nutrients. It is a labile component of the soil organic fraction containing 1 to 3% of the soil carbon and up to 5% of the total soil N. The microbiologically mediated processes affect ecosystem functions associated with nutrient cycling, soil fertility, global C change and soil organic matter turnover. The size and activity of the soil microbial biomass must be assessed to fully understand nutrient flux in managed and natural ecosystems.

Soil microbial biomass estimations are useful in investigations that compare temporal nutrient fluctuations along natural and perturbed gradients. The effect of tillage, crop rotations and soil type on organic carbon and nutrient turnover can be assessed by following nutrient pools and activity associated with the soil microbial biomass.

Measurement of soil aeration

Oxygen Diffusion Rate (ODR) - the rate at which O₂ in soil air is replenished. ODR decreases with soil depth.

Measurement of ODR in soil

Lemon and Erickson (1952) devised a method for measuring oxygen diffusion in the soil system with the help of platinum micro electrode

Principle

When a certain potential is applied across the platinum electrode and a reference electrode inserted in the soil, oxygen is reduced at the platinum surface. The electric current flowing between two electrodes is proportional to the rate of oxygen reduction. The later, in turn, is related to the rate of oxygen diffusion to the electrode. The oxygen diffusion rate (ODR) is calculated from the measured electric current with the following equation.

The ratio of soil air-to-soil water permeability indicates the magnitude of breakdown of structure as a result of wetting. A value of one indicates no change in structure and a value greater than one reflects a deterioration of soil structure.

Principle

The permeability of soil to air can be obtained essentially in the same way as the permeability of soil to water. The measurement of permeability of soil to air involves the preparation and placement of the soil in a suitable container with provision for monitoring pressure differential across the sample and the rate of flow of air through it. For steady state case, this involves measurement of inlet and outlet pressures and the volume flux of air. The suitable form of the Darcy’s equation for calculating permeability of soil to air is:

Introduction

Measurement of pH of a solution and preparation of different types/strength of buffers are common practices in a laboratory, particularly in the Biochemistry and Molecular Biology laboratories. Therefore, in this chapter you will be acquainted with the procedures of measuring pH of a solution as well as preparation of some of the commonly used buffers in a laboratory.

Potential or Power of Hydrogen Ion (pH)

Measurement of pH of a solution is measuring the molar concentration of hydrogen ion [H+] in the solution, which is an indication of the acidity or basicity of the solution. The symbol pH stands for “power of hydrogen” and numerical value for pH is just the negative logarithm of the molar concentration of hydrogen ions [H+]. The ionic product of water (Kw ) is the basis for the pH scale. The total hydrogen ion concentration from all the sources and it can be experimentally measured.

The pH scale designates the concentration of H+ (and thus of OH−) in an aqueous solution, which ranges between 1.0 M H+ and 1.0 M OH−. The term pH is defined by the expression

Thus, the ionic product of water makes it possible to calculate the concentration of H+, with given concentration of OH−, and vice versa. The value of 7 for pH of a neutral solution is not an arbitrarily chosen figure; it is derived from the absolute value of the ionic product of water. A solution having pH greater than 7 is basic, and the concentration of OH− is greater than that of H+. A solution having a pH less than 7 is acidic.

Introduction

Various organic orthophosphoric mono-and di-esters in soils are hydrolyzed when incubated with toluene-treated or irradiated soils, indicative of phosphatase activity. Assays have been identified, based on the rates of release of orthophosphate. Phosphatase activities of field soils showed little or no variation with season but were influenced by the cropping system and nature of the plant cover. Activities generally increased after the addition of inorganic and organic fertilizers to soils. However, inhibition of phosphatase by phosphatic fertilizers and by liming of soils (application of ca and Mg) has been reported. Phosphatase activities were directly related to the organic-P of soils but were not consistently related to available-P contents.

Phosphatases have been used to describe a broad group of enzymes that catalyze the hydrolysis of both esters and anhydrides. These are classified into five categories

Photosynthesis is an important physiological process associated with plant growth and productivity. During the process of photosynthesis, the solar energy is trapped and converted into chemical potential which is later used for the reduction of CO₂ into carbohydrates. The powerful reductant, NADPH that is needed for carbon reduction is generated by the light driven reactions of the chloroplast lamellar system. Photosynthesis can be summarized as follows.

Photosynthetically active radiation (PAR) is the radiation in the 400-700 nm wave band. For plants, 400-700 nm wave band of the light spectrum is very useful because of photosynthesis activity in this band. A simple integral relationship exists between the number of molecules changed photo-chemically and the photons absorbed within the requisite wave bands regardless of photon energy. Net photosynthesis rates are found to be almost linearly proportional to the radiation intercepted, which can be measured by line quantum sensor.

Pressure of air at a given place is the force exerted against a surface by continuous collision of gas molecules. Pressure may be defined as the force per unit surface area.

Rainfall is precipitation (falling of any type of condensed moisture to the ground) in the form of liquid drops larger than 0.5 mm in diameter falling on the earth surface. Ordinary rain drop size varies from 0.5-4.0 mm in diameter. Rainfall is measured in term of depth of rain water (millimeters) on a solid surface provided that rain water is neither allowed to percolate nor runoff or loss in any form.

In previous section, we discussed about the concept of the reliability and its importance. In this section, we will discuss about different types of reliability and procedures for estimation of the reliability. We already discussed that one cannot measure the reliability but of course it can be estimated.

Aim:- To know the measurement for preparation of an appropriate size of ring of Thomas splint for a large animal.

Objective: Measurement of an appropriate size Thomas splint essential to avoid complications like tight fitting which may affect bone healing.

Materials required: 6mm G.l. wire, jute thread

The moisture content is the amount of water in the seed and is usually expressed as a percentage. It can he expressed on either a wet weight basis (where it is expressed as a percentage of the fresh weight of the seed) or on a dry weight basis (where it is expressed as a percentage of the dry weight of the seed). The seed moisture content is the most vital parameter, which influence the seed quality and storage life of the seed. Seed moisture content is closely associated with several aspects of physiological seed quality. For example, it is related to seed maturity, optimum harvest time, mechanical damage, economics of artificial seed drying, seed longevity and insect & pathogen infestation.

Introduction
• A cell is the most basic structural and functional unit of life. These are of two types:
i) Prokaryotic cells– Prokaryotes are those cells which lack a membrane bound nucleus and other membrane bound cell organelles. These cells are primitive cells. Examples, bacterial cells, archaeal cells.
ii) Eukaryotic cells– Eukaryotes are those cells which have distinct membrane bound organelles. These are advanced cells. Example, animal cells, plant cells, fungi.
• A microorganisms (from the Greek: mikros, “small” and organism’s, “organism”) are those small living organisms which cannot be seen with naked eyes. These are of two types:
i) Single cell– Organism made up of a single cell.
ii) Multi-cellular– Organism made up of multiple cells.
Shape and Arrangement of Bacterial Cells
• Prokaryotes display following shapes
• Spherical cells called Cocci
• Cylinders called rods or Bacilli
• Coma shaped called Vibrio
 

Snow is precipitation of solid water, mainly in the form of branched hexagonal crystals or stars. It is “precipitation of white opaque grains of ice”. Measurement of snow cover is related to runoff estimation and also important for hilly agriculture.

4.1. Snowfall

It is the amount of fresh snow deposited over a specified period (generally 24 hours). The measurements relate to depth and water content of the snowfall.

The information on soil-water content is necessary from the point of view of efficient water management of crop production as water required by crops is to be met from the water stored in their root zone. Soil water content changes periodically as a result of changes in field water balance components namely, precipitation, irrigation, evapotranspiration, runoff and deep percolation. Crop growth is adversely affected if the soil water depletes below certain level. For selection of crops, deciding of irrigation level and frequency of irrigation, the assessment of water content of soil is important.

Water is an important input in crop production. It acts as solvent, reactant and used for transpiration and maintaining cell turgidity. Hence, knowledge of soil moisture is essential for making irrigation scheduling. For determining soil moisture status, the commonly used methods and instruments are discussed along with their advantages and disadvantages. The soil moisture can be measured by determining either the soil water content or the soil water potential. The measurement of soil water content is an estimation of the mass or volume of water in the soil, while the soil water potential is an expression of the soil water energy status. The relation between content and potential is not universal and depends on the characteristics of the local soil, such as soil density and soil texture. We can measure soil moisture content both by direct and indirect methods. In direct method, we remove the water from the soil sample by evaporation and the amount removed is determined. This method is popularly known as gravimetric method. We measure property of soil that is affected by soil water content under the indirect methods. Indirect methods employ tensiometric, nuclear (neutron and gamma radiations), electromagnetic (radar and time domain reflectometers), hygrometric (electrical resistance, capacitance, Infrared absorption) techniques besides remote sensing for making soil water models. In the following paragraphs both the methods of soil water measurement has been discussed.

Tensiometer is a device to measure soil moisture tension or equivalent negative pressure of water in the soil. A tensiometer consists of a tube sealed at one end by a porous ceramic cup which is in contact with the soil and a vacuum gauge or a manometer connected at the other end above the soil surface. When the tensiometer is filled with water, the manometer or gauge will read zero tension. When such a tensiometer is placed in an unsaturated soil, the soil in contact with the porous ceramic cup will immediately start sucking water through the porous cup wall. The water in the soil pores immediately establishes hydraulic equilibrium with the water in the cup through saturated pores of the cup wall. Water and solutes can f low through the pores of the cup wall but not the air within the working range of the tensiometer. Water could be sucked from the tensiometer by the soil until vacuum created inside the tensiometer is just sufficient to overcome the suction of the soil. At equilibrium, the tensiometer reads directly the amount of soil suction. The outf low of water from the cup is very little. The effective range of the tensiometer is 0 to 0.85 bars depending on quality of the porous cup.

The measurement of soil moisture is needed to determine when to irrigate and the amount of water needed when irrigating, to evaluate evapotranspiration, and to monitor soil matric potential. The soil moisture is measured in two ways- direct and indirect methods as follows:

The surface of the earth gets heated up during the day and gets cooled during the night causing diurnal changes in the top layers of the soil. Soil temperature is an important part of micro-environment, where plant roots grow and capture the water and nutrients and thus, it affects the plant growth and yield. During crop germination also soil temperatures play vital role. Since the heat regimes of these layers are governed by the soil temperature, the measurement of soil temperature becomes extremely important.

Soil temperature plays an important role in plant growth. Solar radiation received on the earth surface raises the temperature of the soil surface from morning to solar noon followed by a decline until the next morning. Soil temperature gradients established on the surface lead to flow of heat downwards causing a rise in temperature of lower layers. These variations in temperature affect germination, emergence and further growth of plants. Several types of thermometers such as mercury or liquid in glass, bimetallic, bourdon gauge, thermocouples and electrical resistance have been used in soil research but the use of thermocouples and thermistors has been found most useful. A brief description of different types of thermometers used in measurement of soil temperature is given below:

Liquids in Glass Thermometer

A liquid-in-glass thermometer (Figure 20.1) consists of a capillary glass tube with a bulb at one end filled with a thermometric liquid (mercury), vacuumed and sealed. By reading the position of the liquid level on a scale the temperature value can be obtained.

The solar energy is the main source of energy for the processes occurring at the earth surface and in its atmosphere. Crop production, is in fact an exploitation of solar radiation and plants are the converters of solar energy into a useful form of energy which is biomass and sustain life providing food, fodder, fiber, fuel, fruits etc. Sun energy fulfills two essential needs of the plants i.e.  (i) light for photosynthesis including many other photo processes and functions of the plants, (ii) thermal conditions required for the normal physiological functions of the plant. Thus, the crop production and agriculture is basically dependent on quality and quantity of radiation.

Water loss from a plant in the form of vapour is known as transpiration. Loss of water vapour mainly from leaf cells through pores but also from the leaf cuticle and through lenticels of the stem. The resistance to diffusion of water vapour through a plant’s stomata is called as stomatal resistance. Whereas, stomatal conductance is a numerical measure of the maximum rate of passage of either water vapour or carbon dioxide through the stomata, or small pores of the plant.

Weather phenomena are not localized, it moves and varies over space and time. The weather over a place or area is the result of far away weather events/conditions. Acquisition of global scale observation, therefore, becomes a pre-requisite for understanding the physics of the weather and also to represent the weather condition over an area at a particular time. Complex three-dimensional models of weather systems can be made by collecting weather data at multiple levels in the atmosphere. Upper-air data are important to know present weather over a place and crucial for weather forecasting.

Wind influences the plant life both physiologically and mechanically. Wind affects plant directly by increasing the transpiration and intake of CO₂. Thus raising the supply of CO₂ to the plants and thereby increase in photosynthesis. However, the increase in photosynthesis is again upto a certain wind speed beyond which its rate become constant. The warm and dry winds increase evaporative loss and cause moisture stress. Lodging is one of severe injury caused by strong winds which causes great yield loss depending upon the stage of crop. This injury is common in paddy, maize, wheat, sorghum and sugarcane. Strong winds damage fruit trees extensively by breaking leaves and twigs and causing fruit drops.

4.1 Learning Objectives
By the end of this chapter, you will be able to:
i) Understand the concepts of Central Tendency and Partition Values;
ii) Identify appropriate measures for different data sets;
iii) Distinguish between different types of means;
iv) Apply Partition Values in data analysis.

4.2 Introduction

Nowadays, the ability to proficiently analyze and interpret data sets is indispensable for strategic decision-making. This chapter, ‘Measures of Central Tendency and Partition Values,’ extends beyond the basics of mean, median, and mode to explore the deeper layers of data analysis through quartiles, deciles, and percentiles. These measures offer a more comprehensive understanding of data distribution, crucial for identifying trends and making precise business predictions. We will unravel how these statistical tools can be effectively employed to dissect and interpret complex data sets, providing business professionals with an enhanced toolkit for informed analysis and decision-making in various business scenarios.

3.1 MEASURES OF CENTRAL TENDENCY (AVERAGES)

When data are presented in raw form or in the form of frequency distribution, they fail to provide a general idea of the data under study. The general idea of statistical methods is to condense the raw data into a form that can convey some meaningful characteristic(s) of the data. Though classification simplifies the data and improves the understanding of the main characteristics in the data, it is still difficult to remember. In any distribution of data, values of a variable may tend to cluster (or concentrate) around a central value. The data must be condensed into a single value. Such presentation of data is called a Central Tendency and the measures devised to consider this tendency are known as Measures of Central Tendency.

An average condenses a frequency distribution or raw data and presents it in a single representative number. It is that single value which is considered as the most representative or typical value for a set of values. Such a value usually lies somewhere near the centre of the group. That is why, an average is usually referred to as a measure of central tendency. It is located at a point around which most of the other values tend to cluster and therefore it is also termed as a measure of central location.

3.1 Introduction

One of the most important objectives of statistical analysis is to summaries the information contained in the data which may be considered either as a population or as a sample (or sub-population). If the set of data consists of all conceivably possible (or hypothetically possible) observations of a certain phenomenon or a variable, we call it as population. If a set of data contains only a part of these observations, that is selected values of a variable, we call it as sample. Frequency distribution and graphical representation summarize to some extent.  They reduce a mass of data to a more understandable form but not to a single value. The aim of this lesson is to determine descriptive measures or statistical constants which will describe the nature of the data.

Measures of central tendency are also known as averages. Averages are defined as statistical constants which enable us to understand in a single effort, the significance of the whole i.e., they are the representative value of the distribution. They give an idea about the concentration of the values in the central part of the distribution.

Five Types of Averages

Arithmetic Mean

It is the sum of all the observations divided by the number of observation.

For individual data or simple series (i.e., series in which all values have single frequency)

One of the most important aspects of describing distribution is the central value around which the observations are distributed. A statistical measure used for representing the centre of central value of a set of observations is known as “Measure of Central Tendency”. This central value is also called as ‘Average’. The commonly used measures of central tendency are as follows;

The central tendency measure is defined as the number used to represent the center or middle of a set of data values. The three commonly used measures of central tendency are the mean, median, and mode.

Measures of location (averages)

The term average refers to any one of several measures of the central tendency of a data set.

• The mean has the disadvantage that its value is influenced by outliers. An outlier is an observation whose value is highly inconsistent with the main body of the data. An outlier with an excessively large value will tend to increase the mean unduly, whilst a particularly small value will decrease it.

• The mean is an appropriate measure of central tendency if the distribution of the data is symmetrical.

The mean will be ‘pulled’ to the right (increased in value) if the distribution is skewed to the right, and ‘pulled’ to the left (decreased in value) if the distribution is skewed to the left.

Literal meaning of dispersion is scatterdness. We study dispersion to have an idea about the homogeneity and heterogeneity of the distribution. Dispersion gives an idea about how much the values of the observation varies from their averages. The series in which the values of the observation differ much from their averages is said to be heterogeneous or highly dispersed. The series in which the value of the observation does not differ much from their averages is said to be homogenous or less dispersed.

There are two types of measures of dispersion:

4.1 Introduction and Measuring

A measure of central tendency exhibits only one of the important characteristics of distribution, namely they typical representative figure to the whole set of its values. This measure alone will not adequately describe a set of observation unless all the observations are alike. Moreover one cannot understand completely about the data set with a measure of central tendency.  Because in real practical situation there may exits a number of sets of observations (or different distributions) whose measures of central tendency are same but they may differ individually from each other in a number of ways.  In particular two sets of values have the same mean but whilst one set of data is grouped close to the mean the other one is more spread out.  The following examples will illustrate this view point clearly.