Answered: At General Hospital, there is some…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

At General 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, 23, 29, 26, 28, 11, 20, 31, 8, 36

Find Q₀

Expert Solution

Step 1

The ascending order of the responses is: 2, 5, 7, 8, 8, 11, 12, 14, 20, 23, 23, 25, 26, 27, 28, 29, 31, 36, 36, 42

The position of first quartile value for even sample size is,

$\begin{array}{rcl} F i r s t q u a r t i l e & = & \frac{25}{100} {(n + 1)}^{t h} R e s p o n s e \\ = & {(\frac{20 + 1}{4})}^{t h} R e s p o n s e \\ = & 5 . 25^{t h} R e s p o n s e \end{array}$

The first quartile is,

$\begin{array}{rcl} F i r s t q u a r t i l e (Q_{1}) & = & 5^{t h} R e s p o n s e + 0.25 (6^{t h} R e s p o n s e - 5^{t h} R e s p o n s e) \\ = & 8 + 0.25 (11 - 8) \\ = & 8 + 0.75 \\ = & 8.75 \end{array}$

The first quartile is 8.75.

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