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Standard IX
Mathematics
Ungrouped Frequency Distribution Table
Question

Prepare the frequency distribution table for the given set of scores:
39,16,30,37,53,15,16,60,58,26,28,19,20,12,14,24, 59,21,57,38,25,36,24,15,25,41,52,45,60,63,18,26,43,36,18,27,59,63,46,25,33,46,42,48,35,64,24.Take class intervals as (10−20),(20−30),.... and answer the following:
(i) What does the frequency corresponding to the third class interval mean?
(ii) What is the size of each class interval? Find the midpoint of the class interval 30−40.
(iii) What is the range of the given set of scores?

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Solution
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Class Interval

Frequency


10-20

20-30

30-40

40-50

50-60

60-70

10

12

7

7

8

3

(i) For Cumulative Frequency 30−40 frequency is 7

(ii) Size is 11

Mid point for cumulative frequency 30−40 is 35.

(iii) Range =70−10=60

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Similar Questions
Q1
Prepare the frequency distribution table for the given set of scores:
39,16,30,37,53,15,16,60,58,26,28,19,20,12,14,24, 59,21,57,38,25,36,24,15,25,41,52,45,60,63,18,26,43,36,18,27,59,63,46,25,33,46,42,48,35,64,24.Take class intervals as (10−20),(20−30),.... and answer the following:
(i) What does the frequency corresponding to the third class interval mean?
(ii) What is the size of each class interval? Find the midpoint of the class interval 30−40.
(iii) What is the range of the given set of scores?
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Q2

Prepare a frequency distribution table for the scores given:

42, 22, 55, 18, 50, 10, 33, 29, 17, 29, 29, 27, 34, 15, 40, 42, 40, 41, 35, 27,

44, 31, 38, 19, 54, 55, 38, 19, 20, 30, 42, 59, 15, 19, 27, 23, 40, 32, 28, 51.

Take the class intervals as 10-20, 20-30, 30-40, 40-50, 50-60.

From the frequency distribution table answer the following questions:

(i) What does the frequency corresponding to the class interval 20-30 indicate?

(ii) In which class intervals are the scores 10, 20 and 30 included?

(iii) Find the range of the scores.

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Q3
The heights of 25 children in centimetre are given below:
174,168,110,142,156,119,110,101,190,102,190,111,172,140,
136,174,128,124,136,147,168,192,101,129,114.
Prepare a frequency distribution table, taking the size of the class interval
as 20, and answer the following:
(i) Mention the class intervals of highest and lowest frequency.
(ii) What does the frequency 6 corresponding to class interval (160−180) indicate?
(iii) Find out the class mark (or midpoint) of (140−160).
(iv) What is the range of heights?
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Q4

The marks scored by 40 candidates in an examination (out of 100) is given below:

75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43, 61,

42, 46, 68, 52, 43, 49, 59, 49, 67, 34, 33, 87, 97, 47, 46, 54, 48, 45,

51, 47, 41, 43.

Prepare a frequency distribution table with the class size 10. Take the class intervals as (30 - 39), (40 - 49), … and answer the following question:

(a) Which class intervals have highest and lowest frequency?

(b) Write the upper and lower limits of the class interval 30-39.

(c) What is the range of he given distribution?

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Q5

The following are the marks scored in a unit test (out of 25). Prepare a frequency distribution table, taking the class intervals as 0-4, 5-9, 10-14, 15-19, 20-24:

21, 14, 3, 7, 23, 18, 24, 16, 18, 17, 20, 10, 17, 18, 21, 23, 19, 12, 14, 9, 16, 18, 12, 14, 11.

From the table (i) find the mid-points of each class interval; (ii) find the class interval having maximum frequency; (iii) find the range of the scores.

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