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 following table gives the marks obtained by $50$ students in a class test

Marks	$11 - 15$	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$	$46 - 50$
Number of students	$2$	$3$	$6$	$7$	$14$	$12$	$4$	$2$

Calculate the mean, median and mode for the above data

Accepted Answer

We make the classes exclusive

Class interval Frequency $f_{i}$ Mid-value $x_{i}$ $f_{i} x_{i}$ Cumulative frequency

$10.5 - 15.5$ $41 - 45$ $13$ $26$ $2$

$15.5 - 20.5$ $3$ $18$ $54$ $5$

$20.5 - 25.5$ $6$ $23$ $138$ $11$

$25.5 - 30.5$ $7$ $28$ $196$ $18$

$30.5 - 35.5$ $16 - 20$ $33$ $462$ $32$

$35.5 - 40.5$ $12$ $41 - 45$ $456$ $44$

$40.5 - 45.5$ $4$ $43$ $172$ $48$

$45.5 - 50.5$ $2$ $48$ $96$ $50$

$\sum f_{i} = 50$ $\sum f_{i} x_{i} = 1600$

Mean:

Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{1600}{50} = 32$

Median:

$N = 50 \Rightarrow \frac{N}{2} = 25$

The cumulative frequency just greater than $25$ is $32$

Hence, the median class is $30.5 - 35.5$

$∴ l = 30.5, h = 5, f = 14, c f = c f$ of preceding class $= 18$

Now, median $= l + \{h \times \frac{(\frac{N}{2} - c f)}{f}\} = 30.5 + \{5 \times \frac{25 - 18}{14}\} = 30.5 + 2.5 = 33$

Mode:

Maximum frequency $= 14$

Hence, modal class is $30.5 - 35.5$

Now, Mode $= x_{k} + h \{\frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 30.5 + 5 \{\frac{14 - 7}{2 (14) - 7 - 12}\} = 30.5 + 3.8 = 34.4$

Class	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$
Frequency	$12$	$22$	$27$	$19$

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	7	5	6	12	8	2

Class	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$
Frequency	$6$	$9$	$15$	$12$	$8$

Class	$84 - 90$	$90 - 96$	$96 - 102$	$102 - 108$	$108 - 114$	$114 - 120$
Frequency	$8$	$10$	$16$	$23$	$12$	$11$

The following table gives the marks obtained by $50$ students in a class test

Marks $11 - 15$ $16 - 20$ $21 - 25$ $26 - 30$ $31 - 35$ $36 - 40$ $41 - 45$ $46 - 50$

Number of students $2$ $3$ $6$ $7$ $14$ $12$ $4$ $2$

Calculate the mean, median and mode for the above data

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Learn and Prepare for any exam you want !

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$3$	$4$	$p$	$3$	$2$

The following table gives the marks obtained by 50 students in a class test Marks 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 Number of students 2 3 6 7 14 12 4 2 Calculate the mean, median and mode for the above data

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Learn and Prepare for any exam you want !

The following table gives the marks obtained by $50$ students in a class test

Marks $11 - 15$ $16 - 20$ $21 - 25$ $26 - 30$ $31 - 35$ $36 - 40$ $41 - 45$ $46 - 50$

Number of students $2$ $3$ $6$ $7$ $14$ $12$ $4$ $2$

Calculate the mean, median and mode for the above data