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Addition of Vectors

The heights o...

Question

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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Solution

The frequency distribution for the given data is as follows:
Answers:
(i) Highest frequency: $(100 - 120)$ ; lowest frequency: $(140 - 160)$ . and $(180 - 200)$ .
(ii) There are $6$ children whose heights are in the range $160 c m$ to $180 c m$ .
(iii) $Class mark = \frac{140 + 160}{2} = 150$

(iv) $Range = highest score - lowest score = 192 - 101 = 91$

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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, 34, 15, 25, 41, 52, 45, 60, 63, 18, 26, 43, 36, 18,

27, 59, 63, 46, 48, 25, 33, 46, 27, 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.

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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?

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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,

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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?

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40

100

75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43, 61, 42, 46

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10

(30 - 39), (40 - 49), . . .

30 - 39

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