Construct the histogram for the following grouped frequency distribution.

Class intervals Frequency

0 - 35 70

35 - 50 15

50 - 60 20

60 - 100 40

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Solution

The correct option is A
Class length is varying in the given distribution, in such case frequency per unit class has to be calculated and histogram has to be constructed with respective heights. For convenience least class length is taken as unit class length.

$Modified length = \frac{Frequency of the class}{Length of that class} \times Least Class length$

Class intervals Frequency Class length Modified Length

0-35 70 35 $\frac{70}{35} \times 10$
=20

35-50 15 15 $\frac{15}{15} \times 10$
=10

50-60 20 10 $\frac{20}{10} \times 10$ =20

60-100 40 40 $\frac{40}{40} \times 10$ =10

Choose suitable scale:
X-axis 1 cm = 1 Min. class interval
Y-axis 1 cm = 4 units

Plot the graph with the help of above table.

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Similar questions

Q. Construct the histogram for the following grouped frequency distribution.

Class intervals	Frequency
0-35	42
35-50	30
50-60	20
60-100	48

Q. Construct the histogram for the following grouped frequency distribution.

Class intervals	Frequency
0 - 35	70
35 - 50	15
50 - 60	20
60 - 100	40

Q. Find the mode of the following distribution.

(i)

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

(ii)

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	45	75	35	25	15

(iii)

Class-interval:	25−30	30−35	35−40	40−45	45−50	50−55
Frequency:	25	34	50	42	38	14

(iv)

Class:	0−10	10−20	20−30	30−40	40−50	50−60	60–70
Frequency:	8	10	10	16	12	6	7

Question 100(ii)

Construct a frequency distribution table for the following weights (in grams) of 35 mangoes, using the equal class intervals, one of them is 40-45 (45 not included):
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37,
53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68
Which weight group has the highest frequency ?

Class-intervals	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$	$100 - 110$
Frequency	$30$	$25$	$45$	$15$	$20$	$40$

Draw a histogram to represent this data:

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Class intervals	Frequency	Class length	Modified Length
0-35	70	35	$\frac{70}{35} \times 10$ =20
35-50	15	15	$\frac{15}{15} \times 10$ =10
50-60	20	10	$\frac{20}{10} \times 10$ =20
60-100	40	40	$\frac{40}{40} \times 10$ =10

Construct the histogram for the following grouped frequency distribution. Class intervals Frequency 0 - 35 70 35 - 50 15 50 - 60 20 60 - 100 40

Construct the histogram for the following grouped frequency distribution.

Class intervals Frequency

0 - 35 70

35 - 50 15

50 - 60 20

60 - 100 40