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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.

Answer :

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.

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, 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.

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

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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- 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, 60. Find the mean, median and mode of this data.
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