Answer to Question #152026 in Statistics and Probability for JG

Question

The following stem-leaf plot represents the age data of a sample of size 40 selected from all faculty members of a local high school, where “4 3” represents 43 years old.

2 122267
3 1234567899
4 123456789
5 123455
6 013556789

Calculate the five-number summary, and find IQR.

Answer 1

21 22 22 22 26 27 31 22 33 34

35 36 37 38 39 39 41 42 43 44

45 46 47 48 49 51 52 53 54 55

55 60 61 63 65 65 66 67 68 69

The five-number summary:

Minimum =21

Maximum = 69

First quartile

$Q_1 = \frac{1}{4}(n+1)^{th} \\ = \frac{41}{4} \\ = 10.25^{th} 10^{th} + 0.25(11^{th}-10^{th}) \\ = 34+0.25(35-34) \\ Q_1 = 34.25 \\ Q_2 = \frac{2}{4}(n+1)^{th} \\ = \frac{41^{th}}{2} \\ = 20.5^{th} \\ = 20^{th} + 0.5(21^{th}-20^{th}) \\ = 44 + 0.5(45-44) \\ Q_2 = 44.05 \\ Median = Q_2 = 44.05 \\ Q_3 = \frac{3}{4}(n+1)^{th} \\ = 30.75^{th} \\ = 55 + 0.75(55-55) \\ = 55 \\ Q_3 = 55 \\ IQR = Q_3-Q_1 \\ = 55 -34.25 \\ = 20.75$