Question

The following data give the numbers of new cars sold by Carpenters Motors Limited during a 20-day sale.
8 5 12 3 9 10 6 12 8 8 4 16 10 11 7 7 3 5 9 11
A. Calculate the values of the three quartiles.
B. Find the value 22nd percentile and interpret it.
C. Prepare a box-and whisker plot (Check for outliers if any).

Answer 1

Given :  data give the numbers of new cars sold by Carpenters Motors Limited during a 20-day sale. 8 5 12 3 9 10 6 12 8 8 4 16 10 11 7 7 3 5 9 11

To find : the values of the three quartiles.

Solution:

8 5 12 3 9 10 6 12 8 8 4 16 10 11 7 7 3 5 9 11

Arranging in ascending order

3  3  4 5 5 6  7 7 8  8 8  9  9  10 10 11  11  12 12 16  

1St Quartile = (5 + 6)/2 = 5.5

Median or 2nd Quartile  =  (8 + 8)/2  = 8

3rd Quartile  = (10 + 11)/2 = 10.5

Value          number of Dots

3                    2

4                    1

5                    2

6                    1

7                    2

8                    3

9                    2

10                   2

11                    2

12                   2

13                   0

14                   0

15                   0

16                   1

16 is an outlier

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