Question

The data represent the age of world leaders on their day of inauguration. Find the​ five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution.

4848 6565 4949 6262 4343 5656 4343 5757 6868 5555 5858 6464 5757 5050 4848

A) The​ five-number summary is:

Create a boxplot of the data.

Choose the correct description of the shape of the distribution.

A.

The distribution is skewed to the right.The distribution is skewed to the right.

B.

The distribution is skewed to the left.The distribution is skewed to the left.

C.

The distribution is roughly symmetric.The distribution is roughly symmetric.

D.

The shape of the distribution cannot be determined from the boxplot.

Answer 1

A) The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

43   43   48   48   49   50   55   56   57   57   58   62   64   65   68   

So, the minimum is 43.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

43   43   48   48   49   50   55   56   57   57   58   62   64   65   68   

So, the bottom half is

43   43   48   48   49   50   55   

The median of these numbers is 48.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

43   43   48   48   49   50   55   56   57   57   58   62   64   65   68   

So, the median is 56 .

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

43   43   48   48   49   50   55   56   57   57   58   62   64   65   68   

So, the upper half is

57   57   58   62   64   65   68   

The median of these numbers is 62.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

43   43   48   48   49   50   55   56   57   57   58   62   64   65   68   

So, the maximum is 68.

From boxplot we see that it is left skewed

So answer here is

B. The distribution is skewed to the left.