Find the measures of center for following.

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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

Find the measures of center for following.

Expert Solution

Step 1-Mode

The frequency distribution (table) is given below.

The value of mode is required here.

Since the first column ( data) consists of the classes (70-74, 75-79,...), let's convert it to class boundaries (continuous classes) then find the mode.

Here, the modal class (a class with the highest frequency ) is 104.5-109.5.

(Note: here highest frequency is 21, so modal class will be 104.5-109.5)

The formula for mode is as follows:

$Mode = l + [\frac{fm - f 1}{2 fm - f 1 - f 2}] \times h$

Where,

l= lower boundary of modal class =104.5

fm = frequency of modal class =21

f1= frequency of pre-modal class =10

f2=frequency of post-modal class =11

h=class width=109.5-104.5 = 5

Therefore, the mode will be:

$\begin{array}{rcl} Mode & = & l + [\frac{fm - f 1}{2 fm - f 1 - f 2}] \times h \\ = & 104.5 + [\frac{21 - 10}{2 \times 21 - 10 - 11}] \times 5 \\ = & 104.5 + [\frac{11}{21}] \times 5 \\ = & 104.5 + 2.619048 \\ = & 107.119048 \\ = & 107.1190 (till 4 decimal places) \end{array}$

Hence, the value of mode is 107.1190.

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