Name: Mean of Grouped Data: Example
Uploaded: 2019-07-19
Duration: 5 min 16 s
Description: Want to find out how to calculate the mean of grouped data when the class intervals are different? Watch this interesting video and learn more!

Question

Find the mean and mode of the following frequency distribution:

Score	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of students	$4$	$28$	$42$	$20$	$6$

Accepted Answer

$\begin{matrix} Class interval & Number of students (f_{i}) & Class mark (x_{i}) & f_{i} x_{i} \\ 20 - 30 & 4 & 25 & 100 \\ 30 - 40 & 28 & 35 & 980 \\ 40 - 50 & 42 & 45 & 1890 \\ 50 - 60 & 20 & 55 & 1100 \\ 60 - 70 & 6 & 65 & 390 \\ Total & Σ f_{i} = 100 & Σ f_{i} x_{i} = 4460 \end{matrix}$

So, the mean $\bar{x}$ of the given data is given by $\bar{x} = \frac{Σ f_{i} x_{i}}{Σ f_{i}} = \frac{4460}{100} = 44.6$ marks

Here the maximum class frequency is $42,$ and the class corresponding to this frequency is $40 - 50 .$ So, the modal class is $40 - 50$

Now, modal class $40 - 50$ . Lower limit $l$ of modal class $= 40$ , class size $(h) = 10$

$f_{1} = 42, f_{0} = 28, f_{2} = 20$

Now, let us substitute these values in the formula:

$Mode = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 40 + (\frac{42 - 28}{2 \times 42 - 28 - 20}) \times 10$

$= 43.89$

Score	$10 - 25$	$25 - 40$	$40 - 55$	$55 - 70$	$70 - 85$	$85 - 100$
Number of students	$6$	$20$	$44$	$26$	$3$	$1$

Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Rajasthan Board-2018

Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Rajasthan Board-2018

Questions from Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Rajasthan Board-2018 with Hints & Solutions

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Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f_{i}$	$6$	$10$	$13$	$7$	$4$