Question

Here's the data (sorted) of the ages of 91 women who won the Oscar for Best Actress in a Leading Role:

21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81

Give the five number summary.

A. 21, 26, 36, 81, 91
B. 21, 28, 33, 41, 81
C. 21, 26, 30, 54, 81
D. 11.8, 21, 33, 36, 91

Answer 1

B. 21, 28, 33, 41, 81

Explanation:

Data : 21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81

Five number summary includes :

1. Minimum vale

2. First Quartile

3. Median : mid value of the given data is 46th term = 33

4.Third Quartile

5.Maximum value

Solution :

1. Minimum vale : smallest value of data = 21

2. First Quartile: median of the data (first number to the actual median) i.e. from 1st term to 46th term

Median for even number of terms :
`((n)/(2)th+((n)/(2)+1)th)/(2)`

n = 46

so, median =
`((46)/(2)th+((46)/(2)+1)th)/(2)`

=
`(23th+24th)/(2)`

=
`(28+28)/(2)`

=
`(56)/(2)`

=
`28`

Thus first quartile = 28

3. Median : mid value of the given data(ages of 91 women) is 46th term = 33

4.Third Quartile :median of the data (46th number[actual median] to the 91th)

Median for even number of terms :
`((n)/(2)th+((n)/(2)+1)th)/(2)`

n = 46

so, median =
`((46)/(2)th+((46)/(2)+1)th)/(2)`

=
`(23th+24th)/(2)`

=
`(41+41)/(2)`

=
`(82)/(2)`

=
`41`

Thus third quartile = 41

5.Maximum value : highest value of data = 81

Thus the five number summary is 21, 28, 33, 41, 81

Hence Option B is correct