Ex.14.4 Q6 Statistics Solution - NCERT Maths Class 9

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Question

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.

Text Solution

Reasoning:

Extreme values in the data affect the mean. This is one of the weaknesses of the 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.

Steps:

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 the mean of the data as median gives a better estimate of average in this case.

(i) Consider the following example − the following data represents the heights of the members of a family.

\(\begin{align} {\rm{154}}{\rm{.9 cm, 162}}{\rm{.8 cm, 170}}{\rm{.6 cm, 158}}{\rm{.8 cm, 163}}{\rm{.3 cm, 166}}{\rm{.8 cm, 160}}{\rm{.2 cm}}\end{align} \)

In this case, it can be observed that the observations in the given data are close to each other.

Therefore, mean will be calculated as an appropriate measure of central tendency.

(ii) The following data represents the marks obtained by \(12\) students in a test.

\(\begin{align} 48,{\rm{ }}59,{\rm{ }}46,{\rm{ }}52,{\rm{ }}54,{\rm{ }}46,{\rm{ }}97,{\rm{ }}42,{\rm{ }}49,{\rm{ }}58,{\rm{ }}60,{\rm{ }}99\end{align} \)

In this case, it can be observed that there are some observations which are very far from other observations. Therefore, here median will be calculated as an appropriate measure of central tendency.

 

  
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