Question

Find the mean, median and mode of the following data:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$4$	$4$	$7$	$10$	$12$	$8$	$5$

Accepted Answer

To find the mean let us put the data in the table given below:

Class Frequency $(f_{i})$ Class mark $(x_{i})$ $f_{i} x_{i}$

$0 - 10$ $4$ $5$ $20$

$10 - 20$ $4$ $15$ $60$

$20 - 30$ $7$ $25$ $175$

$30 - 40$ $10$ $35$ $350$

$40 - 50$ $12$ $45$ $540$

$50 - 60$ $8$ $55$ $440$

$60 - 70$ $5$ $65$ $325$

Total $\sum_{} f_{i} = 50$ $\sum_{} f_{i} x_{i} = 1910$

Mean = $\frac{\sum_{} f_{i}}{\sum_{} f_{i} x_{i}}$
$= 1910 / 50$
$= 38.2$
Thus, the mean of the given data is $38.2$ .

Now, to find the median let us put the data in the table given below:

Class frequency $(f_{i})$ Cumulative frequency $(c f)$

$0 - 10$ $4$ $4$

$10 - 20$ $4$ $8$

$20 - 30$ $7$ $15$

$30 - 40$ $10$ $25$

$40 - 50$ $12$ $37$

$50 - 60$ $8$ $45$

$60 - 70$ $5$ $50$

Total $N = \sum_{} f_{i} = 50$

Now, $N = 50 \Rightarrow N / 2 = 25$ .
The cumulative frequency just greater than $25$ is $37$ and the corresponding class is $40 - 50$ .
Thus, the median class is $40 - 50$ .
$∴ l = 40, h = 10, N = 50, f = 12$ and $c f = 25$ .

Now,
Median $= l + ((N / 2 - c f) / (f)) \times h$
$= 40 + ((25 - 25) / 12) \times 10$
$= 40$
Thus, the median is $40$ .

We know that,
$M o d e = 3 (m e d i a n) - 2 (m e a n)$

$= 3 \times 40 - 2 \times 38.2$

$= 120 - 76.4$

$= 43.6$

Hence, Mean $= 38.2,$ Median $= 40$ and Mode $= 43.6$

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency	$6$	$8$	$10$	$12$	$6$	$40 - 50$	$3$

Class	$0 - 50$	$50 - 100$	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$
Frequency	$2$	$3$	$5$	$6$	$5$	$3$	$1$

Marks obtained	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$
no. of students	$7$	$31$	$33$	$17$	$11$	$1$

Height in cm	$120 - 130$	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$
No. of girls	$2$	$8$	$12$	$20$	$8$

Daily income (in Rs)	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
No. of workers	$12$	$14$	$8$	$6$	$10$

R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 18D

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 18D

Questions from R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 18D with Hints & Solutions

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Daily expenditure (in Rs)	Number of households
$100 - 150$	$6$
$150 - 200$	$7$
$200 - 250$	$12$
$250 - 300$	$3$
$300 - 350$	$2$