# NCERT Class 12 Practical Geography Chapter 2 Data Processing YouTube Lecture Handouts Part 2

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## Median (Ungrouped Data)

 50 40 15 15 5

### Median (Grouped Data)

 Class Units(f) 0 - 10 2 10 - 20 4 20 - 30 3 30 - 40 1 40 - 50 5

M = Median for grouped data

l = Lower limit of the median class

h = Interval

f = Frequency of the median class

N = Total number of frequencies or number of observations

c = Cumulative frequency of the pre-median class.

## Mode (Ungrouped Data)

 50 40 15 15 5
• The value that occurs most frequently in a distribution is referred to as mode. It is symbolized as Z or M0. Mode is a measure that is less widely used compared to mean and median. There can be more than one type mode in a given data set.
• The measure 15 occurring three times in the series is the mode in the given dataset. As no other number is in the similar way in the dataset, it possesses the property of being unimodal.
• In second table 40 and 15 both occur twice and hence is bimodal.

### Mode (Grouped Data)

 Class Units(f) 0 - 10 2 10 - 20 4 20 - 30 3 30 - 40 5 40 - 50 1

l = Lower limit of the median class

h = Interval

= maximum Frequency

= frequencies of class preceding the modal class

= frequencies of class following the modal class

Why Do we need to Study Methods of Dispersion?

### Same Mean of 50

 Individual Score A 52 B 55 C 50 D 48 E 45
• The range of the first distribution is 10, whereas, it is 98 in the second distribution. Although, the mean for both the groups is the same, the first group is obviously stable or homogeneous as compared to the distribution of score of the second group, which is highly unstable or heterogeneous. This raises a question whether the mean is a sufficient indicator of the total character of distributions. The examples provide profound evidence that it is not so. Thus, to get a better picture of a distribution, we need to use a measure of central tendency and of dispersion or variability.
• Dispersion refers to the scattering of scores about the measure of central tendency. It is used to measure the extent to which individual items or numerical data tend to vary or spread about an average value
• Dispersion is the degree of spread or scatter or variation of measures about a central value.
• The dispersion serves the following two basic purposes:
• It gives us the nature of composition of a series or distribution
• It permits comparison of the given distributions in terms of stability or homogeneity

The Standard Deviation (s) as an absolute measure of dispersion and Coefficient of Variation (CV) as a relative measure of dispersion, besides the Range are most commonly used measures of dispersion.

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