Class Interval Frequency
$1 - 5$ $3$
$6 - 10$ $8$
$11 - 15$ $13$
$16 - 20$ $18$
$21 - 25$ $28$
$26 - 30$ $20$
$31 - 35$ $13$
$36 - 40$ $8$
$41 - 45$ $6$
$46 - 50$ $4$
Compute the mode of the given data.

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Solution

$C l a s s I n t e r v a l$ $F r e q u e n c y$
$0.5 - 5.5$ $3$
$5.5 - 10.5$ $8$
$10.5 - 15.5$ $13$
$15.5 - 20.5$ $18 (f_{0})$
$20.5 - 25.5$ $28 (f_{1})$
$25.5 - 30.5$ $20 (f_{2})$
$30.5 - 35.5$ $13$
$35.5 - 40.5$ $8$
$40.5 - 45.5$ $6$
$45.5 - 50.5$ $4$
Modal class $= 20.5 - 25.5$ with highest frequency.
Then we have, $l = 20.5, f_{0} = 18, f_{1} = 28, f_{2} = 20, h = 5$
$M o d e = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} -_{f} 2} \times h$

$= 20.5 + \frac{28 - 18}{2 \times 28 - 18 - 20} \times 5$

$= 20.5 + 0.55$
$= 21.05$

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Similar questions

Compute the mode from the following data:
$\begin{matrix} Class interval & 1 - 5 & 6 - 10 & 11 - 15 & 16 - 20 & 21 - 25 & 26 - 30 & 31 - 35 & 36 - 40 & 41 - 45 & 46 - 50 Frequency & 3 & 8 & 13 & 18 & 28 & 20 & 13 & 8 & 6 & 4 \end{matrix}$

Q. Compute the mode from the following data:

Class interval	1-5	6-10	11-15	16-20	21-25	26-30	31-35	36-40	41-45	46-50
Frequency	3	8	13	18	28	20	13	8	6	4

Table 1
Marks	Frequency	Cumulative Frequency
0-10	2	2
10-20	8	10
20-30	12	22
30-40	18	40
40-50	28	68
50-60	22	90
60-70 70-80	6 4	96 100

Table 2

Class (marks )	Frequency
11-15	2
16-20	3
21-25	3
26-30	5
31-35	6
36-40	6
41-45	3
46-50	2
Total	30

Table 3

Time (in min)	Frequency
15	7
20	15
25	17
30	3
35	14
40	2

Table 4

31	42	49	25	29
40	36	24	29	30
40	46	38	34	26
24	22	39	40	21

Which table shows the cumulative frequency distribution?

Q. For the following data obtain the mode.

Weight (in kg)	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$	$46 - 50$	$51 - 55$	$56 - 60$
No. of students	$5$	$4$	$3$	$18$	$20$	$14$	$8$	$3$

Q. Find the median for the following data.

Marks	$11 - 15$	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$
Frequency	$7$	$10$	$13$	$26$	$9$	$5$

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Class Interval	Frequency
$1 - 5$	$3$
$6 - 10$	$8$
$11 - 15$	$13$
$16 - 20$	$18$
$21 - 25$	$28$
$26 - 30$	$20$
$31 - 35$	$13$
$36 - 40$	$8$
$41 - 45$	$6$
$46 - 50$	$4$

$C l a s s I n t e r v a l$	$F r e q u e n c y$
$0.5 - 5.5$	$3$
$5.5 - 10.5$	$8$
$10.5 - 15.5$	$13$
$15.5 - 20.5$	$18 (f_{0})$
$20.5 - 25.5$	$28 (f_{1})$
$25.5 - 30.5$	$20 (f_{2})$
$30.5 - 35.5$	$13$
$35.5 - 40.5$	$8$
$40.5 - 45.5$	$6$
$45.5 - 50.5$	$4$

Class IntervalFrequency1−536−10811−151316−201821−252826−302031−351336−40841−45646−504 Compute the mode of the given data.

Class Interval Frequency
$1 - 5$ $3$
$6 - 10$ $8$
$11 - 15$ $13$
$16 - 20$ $18$
$21 - 25$ $28$
$26 - 30$ $20$
$31 - 35$ $13$
$36 - 40$ $8$
$41 - 45$ $6$
$46 - 50$ $4$
Compute the mode of the given data.