Question

At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were 23 2 5 14 25 36 27 42 12 8 7 15 29 26 28 11 20 31 8 36

Find the interquartile range

. POSSIBLE ANSWERS vvvvvv 19.0 38.0 22.5 19.5 37.5

Answer 1

Solution :

Arranging Observations in the ascending order, We get :
2,5,7,8,8,11,12,14,15,20,23,25,26,27,28,29,31,36,36,42

Here, n=20

Q1 = (n + 1/4)th value of the observation

= (21 / 4)th value of the observation

= (5.25)th value of the observation

= 5th observation + 0.25[6th - 5th]

= 8 + 0.25[11 - 8]

=8+0.25(3)

= 8 + 0.75

= 8.75

Q3 = (3(n+1) / 4)th value of the observation

= (3⋅21 / 4)th value of the observation

= (15.75)th value of the observation

= 15th observation + 0.75[16th -15th]

= 28 + 0.75[29 - 28]

= 28 + 0.75(1)

= 28 + 0.75

= 28.75

Interquartile range = Q3 - Q1 = 28.75 - 8.75 = 19.5