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.

56

64

48

59

63

68

65

64

68

69

60

45

62

47

57

The​ five-number summary is

nothing

​,

nothing

​,

nothing

​,

nothing

​,

nothing

.

Answer 1

The five-point summary has five values which consist of minimum value, Q1 which is the 25th percentile value of the data set, Q2 which is the median and the 50th percentile value, Q3 or the 75th percentile value and the maximum value of the data set.

The Five-point summary is calculated by finding the position of the respective values as:

Minimum = 45

Q1 position is calculated as the median of the first half of the dataset which is the 4th value as:

Q1 = 57

Q2 :

The Median or Q2 is at 50th percentile which is between 7th and 8th value hence the Q2 is calculated as:

Median = (62+63)/2 = 62.5

Q3 place is calculated as the median of the 2nd half which is the 12th position hence:

Q3 = 65

Minimum: 45
Quartile Q1: 57
Median: 62.5
Quartile Q3: 65
Maximum: 69

The Box-plot is plotted as:

From the box-plot of the given dataset, the distribution can be said to be skewed to left since, and plot the median is more towards the right and hence most data fall on the right side of the data set.

So, we can say the distribution is non-symmetrical.