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.

Solution:

Extreme values in the data affect the mean. This is one of the drawbacks of mean, so if the data has a few points which are very far from most of the other points (like 1,7,8,9,9), then the mean is not a good representative of this data.

Since the median and mode are not affected by extreme values present in the data, they give a better estimate of the average in such a situation.

When any data has a few observations such that these are very far from the other observations in it, it is better to calculate the median than that of mean as the median gives a better estimate of average in this case.

(i) Consider the following example − The following data represent the heights of the members of a family:

154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm

In this case, 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 12 students in an exam:

48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99

In this case, it can be observed that some observations are very far from the other observations.

Therefore, the mean will not be an appropriate measure of central tendency but the median will be an appropriate measure of central tendency.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 14

Video Solution:

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.

NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4 Question 6

Summary:

For the data 154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm, the mean is an appropriate measure of central tendency whereas, for the data 48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99 the mean is not an appropriate measure of central tendency, but the median is an appropriate measure of central tendency.

☛ Related Questions:

• In a mathematics test given to 15 students, the following marks (out of 100) are recorded:41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60Find the mean, median and mode of this data.
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