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You have learnt in previous chapter that organising and presenting data makes them comprehensible. It facilitates data processing. A number of statistical techniques are used to analyse the data. In this chapter, you will learn the following statistical techniques:
1. Measures of Central Tendency
2. Measures of Dispersion
3. Measures of Relationship
While measures of central tendency provide the value that is an ideal representative of a set of observations, the measures of dispersion take intoaccount the internal variations of the data, often around a measure of central tendency. The measures of relationship, on the other hand, provide the degree of association between any two or more related phenomena, like rainfall and incidence of flood or fertiliser consumption and yield of crops.
Measures of Central Tendency
The measurable characteristics such as rainfall, elevation, density of population, levels of educational attainment or age groups vary. If we want to understand them, how would we do ? We may, perhaps, require a single value or number that best represents all the observations. This single value usually lies near the centre of a distribution rather than at either extreme. The statistical techniquesused to find out the centre of distributions are referred as measures of central tendency. The number denoting the central tendency is the representative figure for the entire data set because it is the point about which items have a tendency to cluster.
Measures of central tendency are also known as statistical averages. There are a number of the measures of central tendency, such as the mean, median and the mode.
1. Choose the correct answer from the four alternatives given below:
(i) The measure of central tendency that does not get affected by extreme values:
(b) Mean and Mode
(ii) The measure of central tendency always coinciding with the hump of any distribution is:
(b) Median and Mode
(iii) A scatter plot represents negative correlation if the plotted values run from:
(a) Upper left to lower right
(b) Lower left to upper right
(c) Left to right
(d) Upper right to lower left
2. Answer the following questions in about 30 words:
(i) Define the mean.
(ii) What are the advantages of using mode ?
(iii) What is dispersion ?
(iv) Define correlation.
(v) What is perfect correlation ?
(vi) What is the maximum extent of correlation?
3. Answer the following questions in about 125 words:
(i) Explain relative positions of mean, median and mode in a normal distribution and skewed distribution with the help of diagrams.
(ii) Comment on the applicability of mean, median and mode (hint: from their merits and demerits).
(iii) Explain the process of computing Standard Deviation with the help of an imaginary example.
(iv) Which measure of dispersion is the most unstable statistic and why?
(v) Write a detailed note on the degree of correlation.
(vi) What are various steps for the calculation of rank order correlation?
1. Take an imaginary example applicable to geographical analysis and explain direct and indirect methods of calculating mean from ungrouped data.
2. Draw scatter plots showing different types of perfect correlations.
Please refer to attached file for NCERT Class 12 Geography Data Processing