# NCERT Solutions for Class 10 Maths Chapter 14 - Statistics

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

Number of Plants | Number of Houses |

0 – 2 | 1 |

2 – 4 | 2 |

4 – 6 | 1 |

6 – 8 | 5 |

8 – 10 | 6 |

10 – 12 | 2 |

12 – 14 | 3 |

**Ans.** 8 plants.

**Q. Thirty women were examined in a hospital by a doctor and the number of heart-beats per minute were recorded and summarised as follows. Find the mean heart-beats per minute.**

Heart-beats per minute | Number of Women |

65 – 68 | 2 |

68 – 71 | 4 |

71 – 74 | 3 |

74 – 77 | 8 |

77 – 80 | 7 |

80 – 83 | 4 |

83 – 86 | 2 |

**Ans.** 75.9 heart-beats per minute.

**Q. The following distribution shows the daily pocket allowance given to the children of a multi-storey building. The average pocket allowance is ₹ 18. Find out the missing frequency.**

Class Interval | Frequency |

11 – 13 | 7 |

13 – 15 | 6 |

15 – 17 | 9 |

17 – 19 | 13 |

19 –21 | f |

21 – 23 | 5 |

23 – 25 | 4 |

**Ans.** 20.

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

No. of Mangoes | No. of Boxes |

50 – 52 | 15 |

53 – 55 | 110 |

56 – 58 | 135 |

59 – 61 | 115 |

62 – 64 | 25 |

Find the mean number of mangoes kept in a packing box.

**Ans.** 50.

**Q. The table below shows the daily expenditure on food of 25 households in a locality. Find the mean expenditure.**

Expenditure | Number of Households |

100 – 150 | 4 |

150 – 200 | 5 |

200 – 250 | 12 |

250 – 300 | 2 |

300 – 350 | 2 |

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

Number of Days | Number of Students |

0 – 6 | 11 |

6 – 10 | 10 |

10 – 14 | 7 |

14 – 20 | 4 |

28 – 38 | 3 |

38 – 40 | 1 |

20 – 28 | 4 |

**Ans.** 12.475 days.

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

Literacy % | Cities |

45 – 55 | 3 |

55 – 65 | 10 |

65 – 75 | 11 |

75 – 85 | 8 |

85 – 95 | 3 |

**Ans.** 69.43%.

**Q. The following distribution shows the daily pocket allowance given to the children of a multi-storey building. The average pocket allowance is ₹ 18. Find out the missing frequency.**

Class Interval | Frequency |

11 – 13 | 7 |

13 – 15 | 6 |

15 – 17 | 9 |

17 – 19 | 13 |

19 –21 | f |

21 – 23 | 5 |

23 – 25 | 4 |

**Ans.** 20.

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

No. of Mangoes | No. of Boxes |

50 – 52 | 15 |

53 – 55 | 110 |

56 – 58 | 135 |

59 – 61 | 115 |

62 – 64 | 25 |

Find the mean number of mangoes kept in a packing box.

**Ans.** 50.

**Q. The table below shows the daily expenditure on food of 25 households in a locality. Find the mean expenditure.**

Expenditure | Number of Households |

100 – 150 | 4 |

150 – 200 | 5 |

200 – 250 | 12 |

250 – 300 | 2 |

300 – 350 | 2 |

**Ans. **₹ 211.

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

Number of Days | Number of Students |

0 – 6 | 11 |

6 – 10 | 10 |

10 – 14 | 7 |

14 – 20 | 4 |

28 – 38 | 3 |

38 – 40 | 1 |

20 – 28 | 4 |

**Ans.** 12.475 days.

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

Literacy % | Cities |

45 – 55 | 3 |

55 – 65 | 10 |

65 – 75 | 11 |

75 – 85 | 8 |

85 – 95 | 3 |

**Ans.** 69.43%.

**Q. If the median of the distribution given below is 28.5 and Σfi = 60, find the value of x and y.**

**Ans.** x = 8, y = 7.

**Q. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons in the age group of 18 to 60 years.**

Class Interval | Frequency |

0 – 10 | 5 |

10 – 20 | x |

20 – 30 | 20 |

30 – 40 | 15 |

40 – 50 | y |

50 – 60 | 5 |

Age (in years) | Number of Policy-holders |

Below 20 | 2 |

Below 25 | 6 |

Below 30 | 24 |

Below 35 | 45 |

Below 40 | 78 |

Below 45 | 89 |

Below 50 | 98 |

Below 60 | 100 |

**Ans.** 35.76 years.

**Q. The lengths of 40 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table. Find the median length of the leaves.**

Length (in mm) | Number of Leaves |

Below 20 | 2 |

118 – 126 | 3 |

127 – 135 | 5 |

136 – 144 | 9 |

145 – 153 | 12 |

154 – 162 | 5 |

163 – 171 | 4 |

172 – 180 | 4 |

**Ans.** 146.75 mm.

**Q. The following table gives the distribution of the life time (in hours) of 400 neon lamps. Find the median life time of a lamp.**

Life time (in hours) | Number of Lamps |

1500 – 2000 | 14 |

2000 – 2500 | 56 |

2500 – 3000 | 5 |

3000 – 3500 | 86 |

3500 – 4000 | 74 |

4000 – 4500 | 62 |

4500 – 5000 | 48 |

**Ans.** 3406.98 hours.

**Q. The following distribution gives the weight (in kg) of 30 students in a class. Find the median weight of the students.**

Weight (in kg) | Number of Students |

40 – 45 | 2 |

45 – 50 | 3 |

50 – 55 | 8 |

55 – 60 | 6 |

60 – 65 | 6 |

65 – 70 | 3 |

70 – 75 | 2 |

**Ans.** 56.67 kg.

**Q. The following data gives the distribution of the total household expenditure (in rupees) of manual workers in a city:**

Expenditure (in Rupees) | Frequency |

1000 – 1500 | 24 |

1500 – 2000 | 40 |

2000 – 2500 | 33 |

2500 – 3000 | 28 |

3000 – 3500 | 30 |

3500 – 4000 | 22 |

4000 – 4500 | 16 |

4500 – 5000 | 7 |

Find the mode of the average expenditure of the families.

**Ans.** ₹ 1847.83.

**Q. The following table shows the ages of the patients admitted to a hospital during a year.**

Ages (in years) | Number of Patients |

5 – 15 | 6 |

15 – 25 | 11 |

25 – 35 | 21 |

35 – 45 | 23 |

45 – 55 | 14 |

55 – 65 | 5 |

Find the mean and mode of the data given above.

**Ans.** Mean = 35.375, Mode = 36.8

**Q. The following distribution provides information about the observed lifetime (in hours) of 225 electrical components. Determine the modal lifetime of the components.**

Lifetime (in years) | Number of Components |

0 – 20 | 10 |

20 – 40 | 35 |

40 – 60 | 52 |

60 – 80 | 61 |

80 – 100 | 38 |

100 – 120 | 29 |

**Ans.** 65.625 hours.

**Q. The following distribution gives the state-wise teacher-student ratio in higher-secondary schools of India. Find the mean and mode from the data.**

Number of Students/Teachers | Number of States/U.T.s |

15 – 20 | 3 |

20 – 25 | 8 |

25 – 30 | 9 |

30 – 35 | 10 |

35 – 40 | 3 |

40 – 45 | 0 |

45 – 50 | 0 |

50 – 55 | 2 |

**Ans.** Mean = 29.2, Mode = 30.6

**Q. The following data shows the number of runs scored in ODI cricket by some of the top batsmen of the world:**

Runs Scored | Number of Batsmen |

3000 – 4000 | 4 |

4000 – 5000 | 18 |

5000 – 6000 | 9 |

6000 – 7000 | 7 |

7000 – 8000 | 6 |

8000 – 9000 | 3 |

9000 – 10000 | 1 |

10000 – 11000 | 1 |

Find the mode of the data.

**Ans.** 4608.7 runs.

**Q. A student noted the number of cars passing through a spot on a road for 100 periods, each of 3 minutes and summarized it in the table given below. Find the mode.**

Number of Cars | Frequency |

0 – 10 | 7 |

10 – 20 | 14 |

20 – 30 | 13 |

30 – 40 | 12 |

40 – 50 | 20 |

50 – 60 | 11 |

60 – 70 | 15 |

70 – 80 | 8 |

**Ans.** Mode = 44.71 cars ≈ 45 cars.