Question

Question 6 Give one example of a situation in which (i) The mean is an appropriate measure of central tendency. (ii) The mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Class 9 - Math - Statistics Page 269"

Answer 1

Central tendency:
The value of the variable which describes the characteristics of the entire data in the associated frequency distribution is called average of the data.

Since, Average represents the entire data so it is also called the central value or measure of Central tendency.
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Solution:


Consider the following examples

i)
The following data represent the height in centimetre of the members of a family
155.9, 163. 8, 170. 6, 159. 8, 162. 3, 166. 8, 160. 2

It can be observed that the observations in the given data are close to each other.
Therefore the mean will be an appropriate measure of Central tendency.

ii)
The following data represents the marks obtained by 13 students in a test
48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99, 96

It can be observed that there are some observations which are very far from other observations.

Therefore the median will be an appropriate measure of Central tendency.

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Hope this will help you.....

Answer 2

Answer:

Mean is not an appropriate measure of central tendency when all the terms of the data are not fairly close to each other.

Let's take an example, we have data of the form:

50, 51, 55, 54, 200.

Mean of this data is equal to 82 which is not close to any of the terms present in the data.

In such a case, median is a better method. Arranging data in the ascending order we get,

50, 51, 54, 55, 200

Clearly, median of this data is equal to 54 which is close to most of the terms present in the data.

Hope it will help u