S.chand Composite Maths books class 8 maths solution chapter 28 Data Handling exercise 28 A

 EXERCISE 28 A

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Q1 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

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Question 1

Write (T) for true or (F) for false. Use the following frequency table.

Age	13	14	15	16	17	18	19
Frequency	3	2	7	2	3	2	1

(i) The frequency of 19 is 1

Sol : T

(ii) The frequency of 14 is 3

Sol : F

(iii) 17 has the lowest frequency

Sol : F

(iv) 16 has a frequency of 2

Sol : T

(v) 15 has the highest frequency

Sol : T

(vi) The frequency of 13 is 3

Sol : T

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Question 2

The ages of all the workers in a certain company are as follows:
23,28,25,21,40,50,50,21,40,50,33,28,41,25,33,37,23,26,41,37,37,21,43,33,37,28,32,33,43,32.
(i) Construct a frequency table for the above data.

Sol :

Ages	21	23	25	26	28	32	33	37	40	41	43	50
Frequency	3	2	2	1	3	2	4	4	2	2	2	3

(ii) How many workers are over 35 years old ?

Sol : 13

(iii) How many workers are under 30 years old ?

Sol : 11

(iv) What is the least age?

Sol : 21 years

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Question 3

Find the mean of the following sets of numbers.
(i)2.5,2.4,3.5,2.8,2.9,3.3,3.6

Sol : 

$\overline{x}=\dfrac{2.5+2.4+3.5+2.8+2.9+3.3+3.6}{7}$

=3

(ii)-6,-2,-1,0,1,2,5,9

Sol : 

$\overline{x}=\dfrac{-6+(-2)+(-1)+0+1+2+5+9}{8}$

=1

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Question 4

Anu received 85, 73, 92, 61 and 89 marks in five tests. What are her mean marks?

Sol :

$\overline{x}=\dfrac{85+73+92+61+89}{5}$

=80 marks

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Question 5

Priya practiced on her sitar 45 minutes, 30 minutes, 60 minutes, 50 minutes and 20 minutes. What was her mean practice time ?

Sol :

$\overline{x}=\dfrac{45+30+60+50+20}{5}$

$=\dfrac{205}{5}=41$ minutes

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Question 6

Find the mean of the first ten prime numbers.

Sol :

First ten prime numbers=2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

$\overline{x}=\dfrac{2+3+5+7+11+13+17+19+23+29}{10}$

$=\dfrac{129}{10}$=12.9

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Question 7

Shikha secured 73, 86, 78 and 75 marks in four tests. What is the least number of points she can secure in her next test if she is to have an average of 80?

Sol :

A.T.Q

Mean of 5 test is 80

Four test marks 73, 86, 78 and 75 and let the fifth test marks be x

∴$\dfrac{73+86+78+75+x}{5}=80$

312+x=80×5

x=400-312=88

∴88 marks will be required in 5th test.

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Question 8

The mean of 5 numbers is 20. if one number is excluded, mean of the remaining numbers becomes 23.Find the excluded number.

Sol :

Let the excluded number be x (5th number)

A.T.Q

Mean of 4 number is 23, which is equal to 

$\dfrac{\text{Sum of 4 numbers}}{4}=23$

Sum of 4 numbers =23×4

Sum of 4 numbers =92...(i)

Mean of 5 numbers is 20, which is equal to 

$\dfrac{\text{Sum of 4 numbers + 5th number }}{5}=20$

Sum of 4 numbers + x=20×5

Sum of 4 numbers + x=100

92+x=100 (From above)

x=100-92=8

Excluded number x= 8

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Question 9

Find the mean of the following distributions
(i)

x	4	6	9	10	15
f	5	10	10	7	8

Sol :

x	f	f.x
4	5	20
6	10	60
9	10	90
10	7	70
15	8	120
	𝝨f=40	𝝨f.x=360

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{360}{40}$

=9

(ii)

x	10	30	50	70	89
f	7	8	10	15	10

Sol :

x	f	f.x
10	7	70
30	8	240
50	10	500
70	15	1050
89	10	890
	𝝨f=50	𝝨f.x=2750

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{2750}{50}$

=55

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Question 10

The following table gives the height in cm and the number of plants of each height. Compute the mean height of the plants.

Height in cm (x)	50	53	61	64	67	70
Number of plants (f)	15	10	18	12	25	20

Sol :

Sol :

x	f	f.x
50	15	750
53	10	530
61	18	1098
64	12	768
67	25	1675
70	20	1400
	𝝨f=100	𝝨f.x=6221

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{6221}{100}$

=62.21 cm