Question

The following are the last 7 days adjusted closing stock prices (in $) for Citigroup: 22, 25, 20, 15, 40, 55, 28 A) Compute the 25th percentile by hand and interpret. B) Compute the sample mean and median by hand. What is the shape of the data set?

Answer 1

(A) The 25th percentile is 20.

(B) The mean of the data set is 20 and the median of the data set is 25. The data set is left-skewed.

Explanation:

The data set arranged in ascending order is:

S = {15, 20, 22, 25, 28, 40, 55}

(A)

Compute the 25th percentile as follows:

`25^(th) \text{Percentile}=[(n+1)/(4)]^(th)obs.\\\\=[(7+1)/(4)]^(th)obs.\\\\=2^(nd)obs.\\\\=20`

Thus, the 25th percentile is 20. This value implies that exactly 25% of the observations are less than 20.

(B)

Compute the sample mean as follows:

`\text{Mean}=(22+25+20+15+40+55+28)/(7)=(205)/(7)=29.29`

Compute the median as follows:

For a set with odd number of observations, the median value if the middle value.

The middle value is 25.

Thus, the mean of the data set is 20 and the median of the data set is 25.

The Mean < Median.

This implies that the data set is left-skewed.