Question

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

Answer 1

Answer:

B. 21, 28, 33, 41, 81

Step-by-step 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 :  $\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}$

n = 46

so, median =  $\frac{\frac{46}{2}th+(\frac{46}{2}+1)th}{2}$

                    = $\frac{23th+24th}{2}$

                    = $\frac{28+28}{2}$

                   = $\frac{56}{2}$

                     = $28$

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 :  $\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}$

n = 46

so, median =  $\frac{\frac{46}{2}th+(\frac{46}{2}+1)th}{2}$

                    = $\frac{23th+24th}{2}$

                    = $\frac{41+41}{2}$

                   = $\frac{82}{2}$

                     = $41$

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