10th Maths 14.1

Chapter 14

Statistics

NCERT Class 10th solution of Exercise 14.2

NCERT Class 10th solution of Exercise 14.3

NCERT Class 10th Maths Projects

Exercise 14.1

Q.1 A survey was conducted by a group of students as a part of their environment awareness programme, 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.

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

Sol. :

`text {Mean  } overline x = (∑f_ix_i)/(∑fi) = 162/20 = 8.1`

`text {Answer:}`

`8.1` plants. We have used direct method because numerical values of `x_i` and `f_i` are small.

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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.

Sol. :

`text{Let the assume mean a = 550 and h = 20`

`text{Mean   }overlinex = a + (∑f_iu_i)/(∑f_i)timesh` 

`= 550+(-12times20)/50` 

`= 550-240/50`

`=550-4.80`

`= 545.20`

`text{Answer:}`

`₹ 545.20.`

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.

Sol. :

`text{Mean  }overlinex = (∑f_ix_i)/(∑f_i)`

`18 = (752+20f)/(44+f)`

`752+20f =792+18f`

`20f-18f=792-752`

`2f=40`

`f=40/2`

`f=20`

`text{Answer:}`

`f= 20`.

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

Sol. :

`text{Let the assume mean a = 75.5 and h = 3`

`text{Mean  }overlinex = a+(∑f_iu_i)/(∑f_i) times h`

`overline x =75.5+(4 times 3)/30`

`overline x = 75.5 + 0.4`

`overline x = 75.9`

`text{Answer:}`

`overline x =75.9`

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.

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

Sol. :

`text{Let, assume mean a = 57 and h = 3`

`text{Mean } overline x = a +(∑f_iu_i)/(sumf_i)`

`overline x = 57 + (25times3)/400`

`overline x = 57 + 3/16`

`overline x = 57 +0.19`

`overline x = 57.19`

`text{Answer:}`
`overline x = 57.19`

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

Find the mean daily expenditure on food by a suitable method.

Sol.:

`text{Let, assume mean a = 225 and h = 50`

`text{Mean }overline x = a + (sum f_iu_i)/(sum f_i) times h`

`overline x = 225 + (-7 times 50)/25`

`overline x = 225 - 14`

`overline x = text{₹ 211}`

`text{Answer:}` 
`overline x = text{₹ 211}`

Q7. To find out the concentration of `SO_2` 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.

Find the mean concentration of `SO_2` in the air.

Sol. :

`text{Mean } overline x = (sumf_ix_i)/(sumf_i)`

`overline x = 2.96/30`

`overline x = 0.099 text{ ppm}`

`text{Answer:}`

`overline x = 0.099 text{ ppm}.`

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.

Sol. :

`text{Mean } overline x = (sumf_ix_i)/(sum f_i)`

`overline x = 499/40`

`overline x = 12.475`

`text{Answer:}`

`overline x = 12.475`

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

Sol. :

`text{Mean} overline x = (sumf_ix_i)/(sum f_i)`

`overline x = 2430/35`

`overline x = 69.43%`

`text{Answer:}`

`overline x = 69.43%`.