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

The table below shows the salaries of $280$ persons.

Salary (in $₹$ thousand)	Number of persons
$5 - 10$	$49$
$10 - 15$	$133$
$15 - 20$	$63$
$20 - 25$	$15$
$25 - 30$	$6$
$30 - 35$	$7$
$40 - 45$	$2$
$45 - 50$	$1$

Calculate the median and mode of the data.

Accepted Answer

First, we construct a cumulative frequency table

Salary (in $₹$ thousand) Number of persons Cumulative frequency $(c f)$

$5 - 10$ $10 - 15$ $49 = c f$

$63$ $f_{m} 133 = f$ $133 + 49 = 182$

$15 - 20$ $63 = f_{2}$ $182 + 63 = 245$

$45 - 50$ $1$ $245 + 15 = 260$

$25 - 30$ $6$ $260 + 6 = 266$

$30 - 35$ $7$ $266 + 7 = 273$

$5 - 10$ $49$ $277 + 2 = 279$

$45 - 50$ $1$ $279 + 1 = 280$

$N = 280$

$∴ \frac{N}{2} = \frac{280}{2} = 140$

(i) Here, median class is $10 - 15$ , because $140$ lies in it.

Lower limit $(i) = 10$ , Frequency $(f) = 133$ ,
Cumulative frequency $(c f) = 49$ and class width $(h) = 5$

$∴ Median = l + \frac{(\frac{N}{2} - c f)}{f} \times h$

$= 10 + \frac{(140 - 49)}{133} \times 5$

$= 10 + \frac{91 \times 5}{133}$

$= 10 + \frac{455}{133} = 10 + 3.421$

$= ₹ 13.421$ (in thousand)

$= 13.421 \times 1000$

$= ₹ 13421$

(ii) Here, the highest frequency is $133$ , which lies in the interval $10 - 15$ , called modal class. Lower limit $(i) = 10$ , class width $(h) = 5, f_{m} = 133, t_{1} = 49, and f_{2} = 63$ .

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

$= 10 + \{\frac{133 - 49}{2 \times 133 - 49 - 63}\} \times 5$

$= 10 + \frac{84 \times 5}{266 - 112} = 10 + \frac{84 \times 5}{154} = 10 + 2.727$

$= ₹ 12.727$ (in thousand)

$= 12.727 \times 1000 = ₹ 12727$

Hence, the median and modal salary are $₹ 13421 and ₹ 12727$ respectively.

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$= ₹ 13.421$
Frequency	$17$	$f_{1}$	$32$	$f_{2}$	$19$

Marks	Frequency
$20 - 30$	$p$
$30 - 40$	$15$
$40 - 50$	$25$
$50 - 60$	$20$
$60 - 70$	$q$
$70 - 80$	$8$
$80 - 90$	$10$

Height (in $cm$ )	Number of Children
$124 - 128$	$5$
$128 - 132$	$8$
$132 - 136$	$17$
$136 - 140$	$24$
$140 - 144$	$16$
$144 - 148$	$12$
$148 - 152$	$6$
$152 - 156$	$4$
$156 - 160$	$3$
$160 - 164$	$1$

Size of Agricultural Holdings (in hec)	Number of families
$0 - 5$	$10$
$5 - 10$	$15$
$10 - 15$	$30$
$15 - 20$	$80$
$20 - 25$	$40$
$25 - 30$	$20$
$30 - 35$	$5$

Rainfall (in cm)	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of days	$22$	$10$	$8$	$15$	$5$	$6$

The table below shows the salaries of $280$ persons.

Salary (in $₹$ thousand) Number of persons

$5 - 10$ $49$

$10 - 15$ $133$

$15 - 20$ $63$

$20 - 25$ $15$

$25 - 30$ $6$

$30 - 35$ $7$

$40 - 45$ $2$

$45 - 50$ $1$

Calculate the median and mode of the data.

Important Questions on Statistics and Probability

Learn and Prepare for any exam you want !

Duration (in s)	Number of calls
$95 - 125$	$14$
$125 - 155$	$22$
$155 - 185$	$28$
$185 - 215$	$21$
$215 - 245$	$15$

Distance (in m)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of students	$6$	$11$	$17$	$12$	$4$

The table below shows the salaries of 280 persons. Salary (in₹thousand) Number of persons 5-10 49 10-15 133 15-20 63 20-25 15 25-30 6 30-35 7 40-45 2 45-50 1 Calculate the median and mode of the data.

Important Questions on Statistics and Probability

Learn and Prepare for any exam you want !

The table below shows the salaries of $280$ persons.

Salary (in $₹$ thousand) Number of persons

$5 - 10$ $49$

$10 - 15$ $133$

$15 - 20$ $63$

$20 - 25$ $15$

$25 - 30$ $6$

$30 - 35$ $7$

$40 - 45$ $2$

$45 - 50$ $1$

Calculate the median and mode of the data.