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.

To do:

We have to 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:

(i) When the values of data do not change much, then the mean is an appropriate measure of central tendency.

 For example,

Marks of 5 students in Mathematics test(out of 10) are $6, 5, 7, 6, 5$

Therefore,

Mean marks $=\frac{6+5+7+6+5}{5}$

$=\frac{29}{5}$

$=5.8$

(ii) When the values of data have very high or low values, then the median is an appropriate measure of central tendency.

 For example,

Marks of 5 students in Mathematics test(out of 100) are $60, 15, 57, 59, 55$

Therefore,

Mean marks $=\frac{60+15+57+59+55}{5}$

$=\frac{246}{5}$

$=49.2$

Arranging the data in ascending order, we get,

$15, 55, 57, 59, 60$

Middle term (3rd term) is 57.

This implies,

Median $=57$ is an appropriate measure of central tendency.