Question

A consumer research project purchased identical items in eight drugstores the mean cost for the purchased items was $155.89 the mode was $154 using the empirical relationship among mean median and mode estimate the median and comment on the skewness of distribution

Answer 1

In case of a moderately skewed distribution, the difference between mean and mode is almost equal to three times the difference between the mean and median.

$\operatorname{mean}-mode=3(\operatorname{mean}-\operatorname{median})$

Using this rule in our problem, we have

$\begin{gathered} 155.89-154=3(155.89-\operatorname{median}) \\ 1.89=3(155.89-\operatorname{median}) \\ 0.63=155.89-\operatorname{median} \\ \operatorname{median}=155.89-0.63 \\ \operatorname{median}=155.26 \end{gathered}$

The median is $155.26.

If a frequency distribution graph has a symmetrical frequency curve, then mean, median and mode will be equal.

In case of a positively skewed frequency distribution, the mean is always greater than median and the median is always greater than the mode.

In case of a negatively skewed frequency distribution, the mean is always lesser than median and the median is always lesser than the mode.

In our problem, the mean is greater than the median

$155.89>155.26$

and the median is greater than the mode

$155.26>154$

Therefore, we have a positively skewed frequency distribution.