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 median and mode of the following frequency distribution:

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

Accepted Answer

Score frequency $10 - 25$ Cumulative frequency $(c f)$

$10 - 25$ $6$ $70 - 85$

$25 - 40$ $20$ $26$

$40 - 55$ $26$ $3$

$55 - 70$ $26$ $96$

$70 - 85$ $3$ $99$

$85 - 100$ $1$ $100$

$N = 100$ . Now, $\frac{N}{2} = \frac{100}{2} = 50$ .

The cumulative frequency just greater than $44$ is $70$ and the corresponding class is $40 - 55$ .
So, $c f = 26, f = 44, L = 40, i = 15$ .
Median, $26$ , where, $L =$ Lower limit of median class, median class is that class where $\frac{N}{2}$ item is lying, $c f =$ Cumulative frequency of the class preceding the median class, $f =$ Frequency of median class, $i =$ Class width

$\Rightarrow M = 40 + (\frac{\frac{100}{2} - 26}{44}) \times 15$

$\Rightarrow M ≃ 48.2$ .

Here the maximum class frequency is $44$ and the class corresponding to this frequency is $40 - 55$ So, the modal class is $40 - 55$

Lower limit $l$ of modal class $= 40$ , class size $(h) = 15$

$f_{1} = 44, f_{0} = 20, f_{2} = 26$

Now, let us substitute these values in the formula:

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

$= 40 + (\frac{44 - 20}{2 \times 44 - 20 - 26}) \times 15$

$= 48.57$

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

Find the median and mode of the following frequency distribution:

Score $10 - 25$ $25 - 40$ $40 - 55$ $55 - 70$ $70 - 85$ $85 - 100$

Number of students $6$ $20$ $44$ $26$ $3$ $1$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the median and mode of the following frequency distribution: Score 10-25 25-40 40-55 55-70 70-85 85-100 Number of students 6 20 44 26 3 1

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the median and mode of the following frequency distribution:

Score $10 - 25$ $25 - 40$ $40 - 55$ $55 - 70$ $70 - 85$ $85 - 100$

Number of students $6$ $20$ $44$ $26$ $3$ $1$