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GSEB Solutions for Class 10 mathematics – Statistics

Contents

GSEB Solutions for Class 10 mathematics – Statistics (English Medium)

Exercise-15.1

Question 1:

Find the mean of the following frequency distribution :GSEB Solutions for Class 10 mathematics - Statistics - 1
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-1

Question 2:

Find the mean wage of 200 workers of a factory where wages are classified as follows :GSEB Solutions for Class 10 mathematics - Statistics - 2
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-2

Question 3:

Marks obtained by 140 students of class X out of 50 in mathematics are given in the following distribution. Find the mean by method of assumed mean method :
GSEB Solutions for Class 10 mathematics - Statistics - 3
Solution :

Let A = 25

Class Frequency (fi) xi di= xi-A fidi
0-10 20 5 -20 -400
10-20 24 15 -10 -240
20-30 40 25 = A 0 0
30-40 36 35 10 360
40-50 20 45 20 400
Total ∑fi= 140 ∑fidi= 120

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-3

Question 4:

Find the mean of the following frequency distribution by step-deviation method :
GSEB Solutions for Class 10 mathematics - Statistics - 4
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-4.1
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-4.2

Question 5:

Find the mean for the following frequency distribution :
GSEB Solutions for Class 10 mathematics - Statistics - 5
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-5

Question 6:

A survey conducted by a student Of B.B.A. for daily income Of 600 families is as follows, find the mean income of a family :GSEB Solutions for Class 10 mathematics - Statistics - 6
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-6

Question 7:

The number of shares held by a person of various companies are as follows. Find the mean :GSEB Solutions for Class 10 mathematics - Statistics - 7
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-7

Question 8:

The mean of the following frequency distribution of 100 observations is 148. Find the missing frequencies f1 and f2 :GSEB Solutions for Class 10 mathematics - Statistics - 8
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-8

Question 9:

The table below gives the percentage of girls in higher secondary science stream of rural areas of various states of India. Find the mean percentage of girls by step-deviation method :
GSEB Solutions for Class 10 mathematics - Statistics - 9
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-9

Question 10:

The following distribution shows the number of out door patients in 64 hospitals as follows. If the mean is 18, find the missing frequencies  f1 and f2 :
GSEB Solutions for Class 10 mathematics - Statistics - 10
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-10

Exercise-15.2

Question 1:

Find the mode for the following Frequency distribution : GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-1
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-1

Question 2:

The data obtained for 100 shops for their daily profit per shop are as follows :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-2
Find the modal profit per shop.

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-2

Question 3:

Daily wages of 90 employees of a factory are as follows :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-3Find the modal wage of an employee.

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-3

Question 4:

Find the mode for the following data : (4 and 5)
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-4
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-4

Question 5:
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-5
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-5

Question 6:

The following data gives the information of life of 200 electric bulbs (in hours) as follows :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.2)-6
Find the modal life of the electric bulbs.

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-6

Exercise-15.3

Question 1:

Find the median for the following . GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-1
Solution :

We will prepare the table containing the cumulative frequency as below:

Value of variable Frequency (f) Cumulative frequency (cf)
12 7 7
13 10 7 + 10 = 17
14 15 17 + 15 = 32
15 18 32 + 18 = 50
16 20 50 + 20 = 70
17 10 70 + 10 = 80
18 9 80 + 9 = 89
19 8 89 + 8 = 97
20 3 97 + 3 = 100

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-1

Question 2:

Find the median for the following frequency distribution :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-2
Solution :

Let us prepare the table containing the cumulative frequencies as below :

Class Frequency (f) Cumulative frequency (cf)
4 – 8 9 9
8 – 12 16 9 + 16 = 25
12 – 16 12 25 + 12 = 37
16 – 20 7 37 + 7 = 44
20 – 24 15 44 + 15 = 59
24 – 28 1 59 + 1 = 60

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-2

Question 3:

Find the median from following frequency distribution : GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-3
Solution :

We will prepare the table containing the cumulative frequencies as below :

Class Frequency (f) Cumulative frequency (cf)
0 – 100 64 64
100 – 200 62 64 + 62 = 126
200 – 300 84 126 + 84 = 210
300 – 400 72 210 + 72 = 282
400 – 500 66 282 + 66 = 348
500 – 600 52 348 + 52 = 400

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-3

Question 4:

The following frequency distribution represents the deposits (in thousand rupees) and the number of depositors in a bank. Find the median of the data :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-4
Solution :

We will prepare the table containing the cumulative frequencies as below:

Deposit
(In thousand Rs.)

Number of depositors
(f)

Cumulative frequency
(cf)

0 – 10 1071 1071
10 – 20 1245 1071 + 1245 = 2316
20 – 30 150 2316+150 = 2466
30 – 40 171 2466 + 171 = 2637
40 – 50 131 2637 + 131 = 2768
50 – 60 8 2768 + 8 = 2776

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-4

Question 5:

The median of the following frequency distribution is 38. Find the value of a and b if the sum of frequences is 400 : GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-5
Solution :

Let us prepare the table containing the cumulative frequency as below:

Class Frequency (f) Cumulative frequency (cf)
10 – 20 42 42
20 – 30 38 42 + 38 = 80
30 – 40 a 80 + a =80+a
40 – 50 54 80 + a + 54 = 134 + a
50 – 60 b 134 + a + b=134 + a + b
60 – 70 36 134 + a + b = 134 + a+b
70 – 80 32 170 + a + b +32 = 202 + a + b

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-5

Question 6:

The median of 230 observations of the following frequency distribution is 46. Find a and b : GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-6
Solution :

We will prepare the table containing the cumulative frequencies as below :

Class Frequency (f) Cumulative frequency (cf)
10 – 20 12 12
20 – 30 30 12+30 = 42
30 – 40 a 42 + a = 42 + a
40 – 50 65 42 + a + 65 =107 + a
50 – 60 b 107 + a + b =107 + a + b
60 – 70 25 107+a+b + 25 = 132 + a + b
70 – 80 18 132+ a + b + 18 = 150 + a + b

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-6

Question 7:

The following table gives the frequency distribution of marks scored by 50 students of class X in mathematics examination of 80 marks. Find the median of the data :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-7
Solution :

Let us prepare the table containing the cumulative frequencies as below:

Class Frequency (f) Cumulative frequency (cf)
0 – 10 2 2
10 – 20 5 2 + 5 = 7
20 – 30 8 7 + 8 = 15
30 – 40 16 15 + 16 = 31
40 – 50 9 31 + 9 = 40
50 – 60 5 40 + 5 = 45
60 – 70 3 45 + 3 = 48
70 – 80 2 48 + 2 = 50

GSEB Solutions for Class 10 mathematics - Statistics-ex(15.1)-7

Exercise-15

Question 1:

In a retail market, a fruit vendor was selling apples kept in packed boxes. These boxes contained varying number of apples. The following was the distribution of apples according to the number of boxes. Find the mean by the assumed mean number of apples kept in the box.
GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-1
Solution :

Let A = 57.5

Number of apples (Class) Number of boxes (fi) Midpoint (xi) di= xi – A fidi
50 – 53 20 51.5 -6 -120
53 – 56 150 54.5 -3 -450
56 – 59 115 57.5 = A 0 0
59 – 62 95 60.5 3 285
62 – 65 20 63.5 6 120
Total ∑fi= 400 ∑fidi= -165

GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-1

Question 2 :

The daily expenditure of 50 hostel students are as follows :GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-2Find the mean daily expenditure of the students of hostel using appropriate method.

Solution :

Let A = 150 and c = 20

Daily expense (in Rs.) Class No. of students (fi) Midpoint (xi) fiui
100 – 120 12 110 -2 -24
120 – 140 14 130 -1 -14
140 – 160 8 150 = A 0 0
160 – 180 6 170 1 6
180 – 200 10 190 2 20
Total ∑fi= 50 ∑fiui= -12

GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-2

Question 3 :

The mean of the following frequency distribution of 200 observations is 332. Find the value of x and y.
GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-3
Solution :

Let A = 375 and c = 50

Class Frequency (fi) Midpoint (xi) fiui
100-150 4 125 -5 -20
150-200 8 175 -4 -32
200-250 X 225 -3 -3x
250-300 42 275 -2 -84
300-350 50 325 -1 -50
350-400 Y 375 = A 0 0
400-450 32 425 1 32
450-500 6 475 2 12
500-550 4 525 3 12
Total ∑fi= 146 + x + y ∑fiui = -130 – 3x

GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-3

Question 4 :

Find the mode of the following frequency distribution : GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-4
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-4

Question 5 :

Find the mode of the following data : GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-5
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-5

Question 6 :

The mode of the following frequency distribution of 165 observations is 34.5. Find the value of a and b.
GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-6
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-6

Question 7 :

Find the mode of the following frequency distribution :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-7
Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-7

Question 8 :

Find the median of the following frequency distribution : GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-8
Solution :

Class Frequency (f) Cumulative Frequency (cf)
10-20 9 9
20-30 11  9 + 11 = 20
30-40 15 20 + 15 = 35
40-50 24 35 + 24 = 59
50-60 19 59 + 19 = 78
60-70 9 78 + 9 = 87
70-80 8 87 + 8 = 95
80-90 5  95+ 5 = 100

GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-8

Question 9 :

The median of the following data is 525. Find the value of x and y, if the sum of frequency is 100 :
GSEB Solutions for Class 10 mathematics - Statistics - EX(15)-9
Solution :

We will prepare the table containing cumulative frequencies as below:

Class Frequency (f) Cumulative frequency (cf)
0 – 100 3 3
100 – 200 4 3+4=7
200 – 300 x 7+x=7+x
300 – 400 12 7+x+12=19+x
400 – 500 17 19+x+17=36+x
500 – 600 20 36+x+20=56+x
600 – 700 9 56+x+9=65+x
700 – 800 y 65+x+y=65+x+y
800 – 900 8 65+x+y+8=73+x+y
900 – 1000 3 73+x+y+3=76+x+y

GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-9

Question 10:

Select a proper option (a), (b), (c) or (d) from given options :

Question 10(1) :

For some data, if Z = 25 and \(\overline{x}\) = 25, then M = ………

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.1

Question 10(2) :

For some data Z – M = 2.5. If the mean of the data is 20, then Z = …….

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.2

Question 10(3) :

If \(\overline{x}\) – Z = 3 and \(\overline{x}\) + Z = 45, then M = …….

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.3

Question 10(4) :

If Z = 24, \(\overline{x}\) = 18, then M = …….

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.4

Question 10(5) :

If M = 15, \(\overline{x}\) = 10, then Z = …….

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.5

Question 10(6) :

If M = 22, Z = 16, then \(\overline{x}\) = …….

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.6

Question 10(7) :

If \(\overline{x}\) = 21.44 and Z = 19.13, then M = ………

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.7

Question 10(8) :

If M = 26, \(\overline{x}\) = 36, then Z = ……..

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.8

Question 10(9) :

The modal class of the frequency distribution given below is ……
GSEB Solutions for Class 10 mathematics - Statistics - EX(15.3)-8
Solution :

c. 30 – 40
Here, the maximum frequency is 17 and the corresponding class of this frequency is 30 – 40. Hence, the modal class is 30 – 40.

Question 10(10) :

The cumulative frequency of class 20-30 of the frequency distribution given in (9) is ………

Solution :

b. 35
Cumulative frequency of class 20 – 30 = frequency of class 20 – 30 and the frequencies of all the classes preceding class 20 – 30 = 7 + 15 + 13 = 35

Question 10(11) :

The median class of the frequency distribution given in (9) is ………

Solution :
GSEB Solutions for Class 10 mathematics - Statistics-ex(15)-10.11

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