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Description: A survey was given to 18 individuals. One question asked about the amount of time the individual exercised per day. The results, in minutes, are shown in the following table. Use the median procedure for finding quartiles to find the first, second, a

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

A survey was given to 18 individuals. One question asked about the amount of time the individual exercised per day. The results, in minutes, are shown in the following table. Use the median procedure for finding quartiles to find the first, second, and third quartiles for the data.

Minutes of exercise per day

48 56 20 22 60 72 14 40 46

46 18 62 64 46 78 34 22 62

Expert Solution

Step 1

The data in the ascending order is 14, 18, 20, 22, 22, 34, 40, 46, 46, 46, 48, 56, 60, 62, 62, 64, 72, and 78

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

$\begin{array}{rcl} First quartile & = & {[\frac{25 (n + 1)}{100}]}^{th} Data value \\ = & {[\frac{25 (18 + 1)}{100}]}^{th} Data value \\ = & 4 . 75^{th} Data value \end{array}$

The first quartile is,

$\begin{array}{rcl} First quartile & = & 4^{th} Data value + 0.75 (5^{th} Data value - 4^{th} Data value) \\ = & 22 + 0.75 (22 - 22) \\ = & 22 \end{array}$

Thus, the first quartile is 22.

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

$\begin{array}{rcl} Second quartile & = & {[\frac{50 (n + 1)}{100}]}^{th} Data value \\ = & {[\frac{50 (18 + 1)}{100}]}^{th} Data value \\ = & 9 . 5^{th} Data value \end{array}$

The second quartile is,

$\begin{array}{rcl} Second quartile & = & 9^{th} Data value + 0.5 (10^{th} Data value - 9^{th} Data value) \\ = & 46 + 0.5 (46 - 46) \\ = & 46 \end{array}$

Thus, the second quartile is 46.

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