Question

Heights of the students in a class are given in the distribution below:

5' - 5'2"      10

5'2" - 5'4" 40

5'4" - 5'6"   25 .

Find:

1. Central Tendency

Answer 1

Solution

Central tendency is the measurement of mean, median and the mode.

(a) Mean.

$\bar X=\dfrac{\sum fX}{\sum f}=\dfrac{400.5}{75}=5.34$

(b) median

$\dfrac{N}{2}=\dfrac{75}{2}=37.5$

Hence the median lies in the class 5.2-5.4

Median$=L+(\dfrac{\frac{N}{2}-pcf}{f})i$

$=5.2+(\dfrac {37.5-11}{40})0 .2$

$=5.3325$

Hence the median height is $5'3"$

(c) Mode

The class with the highest frequency (40) is 5.2-5.4 and hence is the modal class.

Mode$=L(\dfrac{\Delta_1}{\Delta_1+\Delta_2})i$

$M_0=5.2(\dfrac{(40-10)}{(40-10)+(40-25)})0.2$

$=5.333$

Modal height is $5'3"$