The frequency distribution of marks obtained by $60$ students of a class is given.
X $30 - 34$ $40 - 44$ $45 - 49$ $50 - 54$ $55 - 59$ $60 - 64$
f $3$ $5$ $12$ $18$ $14$ $62$

Find mode of the distribution.

42.50

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52.50

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52.05

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42.05

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Solution

The correct option is B $52.50$
The given class intervals should be converted into class boundaries. Since the distribution is regular, the modal class, by inspection, is $49.5 - 54.5$
Further, $L_{m} = 49.5, f_{m} = 18, f_{1} = 12, f_{2} = 12, h = 5$
Mode, $Z = 49.5 + \frac{18 - 12}{(2 \times 18) - 12 - 14} \times 5 = 52.5$

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Similar questions

Q. The frequency distribution of marks obtained by 60 students of a class in a college is given below:

Marks	30−34	35−39	40−44	45−49	50−54	55−59	60−64
No. of Students	3	5	12	18	14	6	2

Q. By taking classes

30 - 40, 40 - 50, 50 - 60, . . .

, construct a frequency table for the following data:

65, 34, 74, 49, 52, 35, 71, 55, 61, 40, 56, 38, 52, 56, 52, 33, 60, 35, 49, 37, 53, 50, 44, 30, 62, 50, 47, 45, 47, 50, 63, 61, 54, 58, 47, 64, 37, 38, 44, 42, 47, 55, 70, 33, 75, 49, 47, 30, 60, 69

Also, construct a combined histogram and frequency polygon for the distribution.

Q. Find the mode of the following frequency distribution of marks obtained by

50

students.

Marks obtained	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
No. of students	$5$	$12$	$20$	$10$	$3$

Q. Following are the marks (out of 100) obtained by 50 students in statistics:

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

make a frequency distribution taking the first class interval as 0-10.

Draw the frequency polygon representing the following frequency distribution.

$\begin{matrix} Class interval & 30 - 34 & 35 - 39 & 40 - 44 & 45 - 49 & 50 - 54 & 55 - 59 Frequency & 12 & 16 & 20 & 8 & 10 & 4 \end{matrix}$
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X	$30 - 34$	$40 - 44$	$45 - 49$	$50 - 54$	$55 - 59$	$60 - 64$
f	$3$	$5$	$12$	$18$	$14$	$62$

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

The frequency distribution of marks obtained by 60 students of a class is given.X30−3440−4445−4950−5455−5960−64f3512181462Find mode of the distribution.

The correct option is B 52.50The given class intervals should be converted into class boundaries. Since the distribution is regular, the modal class, by inspection, is 49.5−54.5Further, Lm=49.5,fm=18,f1=12,f2=12,h=5Mode, Z=49.5+18−12(2×18)−12−14×5=52.5

The frequency distribution of marks obtained by $60$ students of a class is given.
X $30 - 34$ $40 - 44$ $45 - 49$ $50 - 54$ $55 - 59$ $60 - 64$
f $3$ $5$ $12$ $18$ $14$ $62$

Find mode of the distribution.

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18