NCERT Grade 10-Statistics-Answers

NCERT Solutions for Class 10 Maths

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1.    Since, number of plants and houses are small in their values, so we use direct method.

Hence mean number of plants per house is 8.1.

2.    

From given data, Assume mean (a) = 150, Width of the class (h) = 20

Using formula, Mean 

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

3.     

From given data, Assume mean (a) = 18

Hence missing frequency is 20.

4.     

From given data, Assume mean (a) = 75.5, Width of the class (h) = 3

Using formula, Mean 

Hence mean heart beat per minute for women is 78.89.

5.    Since value of number of mangoes and number of boxes are large numerically. So we use step-deviation method.

From given data, Assume mean (a) = 57, Width of the class (h) = 3

Using formula, Mean

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

6.    

From given data, Assume mean (a) = 225, Width of the class (11) = 50

Using formula, Mean 

Hence mean daily expenditure on food is Rs.211.

7.     

From given data, Assume mean (a) = 0.10, Width of the class (h) = 0.04

Using formula, Mean

Hence mean concentration of so2 in air is 0.0987 ppm.

8.    

From given data, Assume mean (a) = 17

Hence mean 12.48 number of days a student was absent.

9.    

From given data, Assume mean (a) = 70, Width of the class (h) = 10

Using formula, Mean

Hence mean literacy rate is 69.43%.

10.   For Mode : In the given data, maximum frequency is 23 and it corresponds to the class interval 35 – 45.

From given data, Assume mean (a) = 30, Width of the class (h) = 10

Using formula, Mean  = 30 + 10 (0.5375) = 30 + 5.375 = 35.37

Hence mode of given data is 36.8 years and mean of the given data is 35.37 years.

Also, it is clear from above discussion that average age of a patient admitted in the hospital is 35.37 years and maximum number of patients admitted in the hospital are of age 36.8 years.

11.   Given: Maximum frequency is 61 and it corresponds to the class interval 60 – 80.

∴ Modal class = 60 – 80

And     l = 60, f1 = 61, f0 =52, f2 = 38 and h = 20

Hence modal lifetimes of the components is 65.625 hours.

12.   For Mode : Here, Maximum frequency is 40 and it corresponds to the class interval 1500 – 2000

∴  Modal class = 1500 – 2000

And     l = 1500, f1 = 40, f0 = 24, f2 = 33 and h = 500

From given data, Assume mean (a) = 2750, Width of the class (h) = 500

Using formula, Mean  = 2750 + 500 (- 0.175) = 2750 – 87.50 = 2662.50

Hence the modal monthly expenditure of family is Rs.1847.83 and the mean monthly expenditure is Rs.2662.50.

13.   For Mode : Here, Maximum frequency is 10 and it corresponds to the class interval 30 – 35.

∴ Modal class = 30 – 35

And     l = 30, f1 = 10, f0 = 9, f2 = 3 and h = 5

From given data, Assume mean (a) = 32.5, Width of the class (h) = 5

Using formula, Mean  = 32.5 + 5 (- 0.65) = 32.5 – 3.25 = 29.25 (approx.)

Hence mode and mean of given data is 30.63 and 29.25. Also from above discussion, it is clear that states/U.T. have students per teacher is 30.63 and on average, this ratio is 29.25.

14.   In the given data, maximum frequency is 18 and it corresponds to the class interval 4000 -5000.

∴ Modal class = 4000 – 5000

And     l = 400, f1 = 18, f0 = 4, f2 = 9 and h = 1000

Hence, mode of the given data is 4608.7 runs.

15.   In the given data, maximum frequency is 20 and it corresponds to the class interval 40 – 50.

∴ Modal class = 40 – 50

And     l = 40, f1 = 20, f0 = 12, f2 = 11 and h = 10

Hence, mode of the given data is 44.7 cars.

16.   For Median:

Here,  which lies in interval 125 – 145.

For Mean:

From given data, Assume mean (a) = 135, Width of the class (h) = 20

Using formula, Mean = 135 + 20 (0.102) = 135 + 2.04 = 137.04

For Made:

In the given data, maximum frequency is 20 and it corresponds to the class interval 125 – 145.

∴ Modal class = 125 – 145

And     l = 125, f1 = 20, f0 = 13, f2 = 14 and h = 20

Hence, median, mean and mode of given data is 137 units, 137.04 units and 135.77 units.

17.    

Here, , also median of the distribution is 28.5,which lies interval 20 – 30.

Hence the value of x and y is 8 and 7 respectively.

18.   

Here,  which lies in interval 35 – 40.

∴ Modal class = 35 – 40

And     l = 35, n = 100, f = 33, cf = 45 and h = 5

Hence median age of given data is 35.76 years.

19.  Since the frequency distribution is not continuous, so firstly we shall make it continuous.

Here, which lies in interval 144.5 – 153.5.

∴ Modal class = 144.5 – 153.5

So,      l = 144.5, n = 40, f = 12, cf = 17 and h = 9

Hence median length of the leaves is 146.75 mm.

20.  

Here, , which lies in interval 3000 – 3500.

∴ Modal class = 3000 – 3500

So,      l = 3000, n = 400, f = 86, cf = 130 and h = 500

Hence median life time of a lamp is 3406.98 hours.

21.  For Median:

Here, which lies in interval 7 – 10.

∴ Modal class = 7 – 10

So,      l = 7, n = 100, f = 40, cf = 36 and h = 3

For Mean:

From given data, Assume mean (a) = 8.5, Width of the class (h) = 3

Using formula, Mean  =  8.5 + 3 (- 0.06) = 8.5 – 0.18 = 8.32

For Mode:

In the given data, maximum frequency is 40 and it corresponds to the class interval 7 – 10.

∴ Modal class = 7 – 10

And      l = 7, f1 = 40, f0 = 30, f2 = 16 and h = 3

Hence, median, mean and mode of given data is 8.05 letters, 8.32 letters and 7.88 letters respectively.

22.    

Here, , which lies in interval 55 – 60.

∴ Modal class = 55 – 60

So,      l = 55, n = 30, f = 6, cf = 13 and h = 5

Hence median weight of the students are 56.67 kg.

23.  

Now, by drawing the points on the graph,

i.e., (120, 12); (140, 26); 160, 34); (180, 40); (200, 50)

Scale: On x – axis 10 units = Rs.10 and on y – axis 10 units = 5 workers

24.   

Hence, the points for graph are:

(38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32), (52, 35)

Scale: On x-axis, 10 units = 2 kg and on y-axis, 10 units = 5 students

From the above graph, Median = 46.5 kg, which lies in class interval 46 – 48.

Here, which lies in interval 46 – 48.

∴ Modal class = 55 – 60

So,      l = 46, n = 35, f = 14, cf = 14 and h = 2

Hence median weight of students is 46.5 kg.

25.   

The points for the graph are:

(50, 100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16)

Scale: On x- axis, 10 units = 5 kg/ha and on y-axis, 10 units = 10 forms.

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