NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics - Future Study Point

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

class 10 statistics 14.1

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics has been brought to you by Future Study Point to help you in your homework, assignments, and forthcoming examination of class 10 CBSE board exam. NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics is one of the greatest input study materials through which you can clear your concepts on Statistics of 10 class CBSE. All questions are solved by an expert in maths by a step-by-step method.

class 10 statistics 14.1

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

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Q1.A survey was conducted by a group of students as a part of their environmental awareness programm in which they collected the following data regarding the number of plants in 20 houses in a locality . Find the mean number of plants per house.

Ex 14.1 class 10

Which method did you use for finding the mean , and why ?

Ans.

No. of PlantsClass Mark (xi)No. of Houses (f)         fixi
0 – 2

2 – 4

4  – 6

6 –  8

8 – 10

10 – 12

12 – 14

 

1

3

5

7

9

11

13

 

1

2

1

5

6

2

3

∑fi   = 20

1

6

5

35

54

22

39

∑fixi= 162

 

We have

Hence mean number of the plants is 8.1

The direct method is proper to use here because the values of observations and their frequencies are small.

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q2.Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

 

ex 14.1 class 10

 

 

 

 

 

 

Ans.

Class IntervalClass Mark (xi)Frequency(fi)       ui=(xi-A)/h       fixi
100 – 120      110      12       -2    -24
120 – 140    130      14      -1    -14
140 – 160    150 = A      8      0     0
160 – 180    170     6      1    6
180 – 200    190    10      2    20
∑fi   = 50∑fiui= -12

Since the class interval is of the size,h= 20 and sum of frequencies is 50, both of them are large therefore applying the step deviation method

Hence the mean daily wages of the workers of the factory  is 145.20

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.

Q3 ex 14.1 class 10

 

 

 

 

 

 

Ans.

Daily pocket allowance (in Rs)Class mark(xi)Frequency(fi)  di=   xi-A       fidi
  11 – 13

13 – 15

15 – 17

17 – 19

19 – 21

21 – 23

23 – 25

  12

14

16

18 = A

20

22

24

  7

6

9

13

f

5

4

  -6

-4

-2

0

2

4

6

  -42

-24

-18

0

2f

20

24

∑fi   = 44 + f∑fidi= 2f – 40

Applying the shortcut method of mean

Where A = 18, ∑fidi= 2f – 40 , ∑fi   = 44 + f  and

2f – 40 = 0⇒ f = 20

Hence missing frequency is 20

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q4.Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

Q4. exercise 14.1 class 10

 

 

 

 

 

 

Ans.

No of heart beats per minuteClass mark(xi)Frequency(fi)fixi

 

65 – 68    66.5   2   133
68 – 71    69.5   4   278
71 – 74   72.5   3   217.5
74 – 77    75.5    8    604
77 – 80    78.5    7   549.5
80 – 83    81.5   4    326
83 – 86    84.5    2    169
∑fi= 30∑fixi= 2277

Applying the direct method for getting the mean of the data

Hence mean of the heartbeats per minute of the women is 75.9

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q5. In a retail market ,fruit vendors were selling mangoes kept in packing boxes.These boxes contained varying number of mangoes .The following was the distribution of mangoes according to the number of boxes.

Q5 ex 14.1 class 10

Find the mean number of the mangoes kept in a packing box. Which method of finding the mean did you choose.

Ans.

No of mangoes  Class mark(xi)   Frequency (fi)   ui=(xi-A)/h     fiui
  50 – 52

53 – 55

56 – 58

59 – 61

62 – 64

  51

54

57= A

60

63

  15

110

135

115

25

  -2

-1

0

1

2

  -30

-110

0

115

50

∑fi400∑fiu= 25

Here we have to apply step deviation because class intervals are not continuous

Hence the mean number of the mangoes kept in a packing box is 57.19

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q6.The table below shows the daily expenditure on food of 25 households in a locality.

q6 ex 14.1 class 10

 

 

 

 

 

 

Find the mean daily expenditure on food by suitable method.

Ans..

 Daily expenditure(in Rs)   Class marks(xi)   Frequency (fi)   ui(xi -A)/h    fiui
  100 – 150  125    4   -2  -8
  150 – 200  175    5   -1  -5
  200 – 250  225   12   0  0
  250 – 300  275   2   1   2
  300 – 350  325    2   2  4
∑fi=25∑fiui= -7

Hence the mean daily expenditure on food is 211

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q7. To find out the concentration of SO2 in the air (in parts per million,i.e PPM) ,the data was collected for 30 localities in a certain city and is presented below.

Q7 ex 14.1 class 10

 

 

 

 

 

 

Ans.

Concentration of SO2(PPM)  Class Mark(xi) Frequency(fi)    ui=(xi -A)/h    fixi
o.oo – 0.04    0.02    4   -2   -8
0.04 – 0.08   0.06    9   -1   -9
0.08 – 0.12   0.10    9    0    0
0.12 – 0.16    0.14    2    1    2
0.16 – 0.20    0.18    4    2    8
0.20 – 0.24

 

    0.22

 

   2

∑fi=30

    3

 

     6

∑fiui=-1

Applying the step deviation method for getting the mean

Hence the average concentration of SO2 is 0.0987

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q8. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Q8. ex 14.1 class 10

Ans.

   No. of days     Class Mark(xi)  Frequency (fi)         fixi
0 – 6       3     11      33
6 – 10      8     10     80
10 – 14      12      7    84
14 -20      17      4   68
20 – 28      24      4   96
28 – 38      33      3   99
38 – 40      39      1    39
∑fi= 40∑fixi= 499

Applying direct method of getting the mean

=12 .48

The mean number of days a student was absent is 12.48

NCERT Solutions For Class 10 Maths Exercise 14.1 Statistics

Q9.The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Q9.ex 14.1 class 10

Ans.

Litracy rate (%) Class mark(xi) Frequency(fi)ui= (xi– A)/h       fixi
    45 – 55    50     3     -2    -6
    55 – 65    60    10    -1   -10
    65 – 75    70 = A    11     0    0
    75 – 85    80    8     1    8
    85 – 95

 

    90

 

     3

∑fi= 35

      2

 

    6

∑fiui=-2

Applying the step deviation method

Where A = 70, h = 10

= 70 – 0.57 = 69.43 %

Hence the mean litracy rate is 69.43 %

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