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Exercises in Chapter 14 statistics Grade 10

Questions in Statistics - Exercise 14.1

**Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute was recorded and summarized as follows. Find the mean heart beats per minute for these women by the step deviation method.

Number of heart beats per minute | 65-6 | 68-71 | 71-74 | 74-77 | 77-80 | 80-83 | 83-86 |
---|---|---|---|---|---|---|---|

Number of women | 2 | 4 | 3 | 8 | 7 | 4 | 2 |

**The table below shows the daily expenditure on the food of 25 households in a locality. Find the mean daily expenditure on food by the step deviation method.

Daily expenditure(in c) | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |
---|---|---|---|---|---|

Number of households | 4 | 5 | 12 | 2 | 2 |

**Consider the following distribution of daily wages of 50 workers of a factory.**

Daily wages (in Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
---|---|---|---|---|---|

Number of workers | 12 | 14 | 8 | 6 | 10 |

**Find the mean daily wages of the workers of the factory by using an appropriate method**.

**A survey was conducted by a group of students as a part of their environment awareness program, 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 by the direct method.**

Number of Plants | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |
---|---|---|---|---|---|---|---|

Number of Houses | 1 | 2 | 1 | 5 | 6 | 2 | 3 |

**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.**

Number of mangoes | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
---|---|---|---|---|---|

Number of boxes | 15 | 110 | 135 | 115 | 25 |

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

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

Literacy rate (in %) | 45-55 | 55-65 | 65-75 | 75-85 | 85-98 |
---|---|---|---|---|---|

Number of cities | Number of cities | 10 | 11 | 8 | 3 |

**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 by the direct method.**

Number of days | 0-6 | 6-10 | 10-14 | 14-20 | 20-28 | 28-38 | 38-40 |
---|---|---|---|---|---|---|---|

Number of students | 11 | 10 | 7 | 4 | 4 | 3 | 1 |

**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:**

Concentration of SO2 ( in ppm) | Frequency |
---|---|

0.00 – 0.04 | 4 |

0.04 – 0.08 | 9 |

0.08 – 0.12 | 9 |

0.12 – 0.16 | 2 |

0.16 – 0.20 | 4 |

0.20 – 0.24 | 2 |

Find the mean concentration of ^{_{SO}}2 in the air by the direct method.

**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.**

Daily Pocket Allowance(in c) | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-35 |
---|---|---|---|---|---|---|---|

Number of children | 7 | 6 | 9 | 13 | f | 5 | 4 |

Questions in Statistics - Exercise 14.2

**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 of the data:**

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 |

**The following data gives the distribution of total monthly household expenditure of 200**
**families of a village. Find the modal monthly expenditure of the families. Also, find the**
**mean monthly expenditure:**

Expenditure | Number of families |
---|---|

1000-1500 | 24 |

1500-2000 | 40 |

2000-2500 | 33 |

2500-3000 | 28 |

3000-3500 | 30 |

3500-4000 | 22 |

4000-4500 | 16 |

4500-5000 | 7 |

**The following table shows the ages of the patients admitted in a hospital during a year:**

Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
---|---|---|---|---|---|---|

Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |

**Find the mode and the mean of the data given above.**

**The following data gives the information on the observed lifetimes (in hours) of 225**
**electrical components:**

Lifetime (in hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
---|---|---|---|---|---|---|

Frequency | 10 | 35 | 52 | 61 | 38 | 29 |

**Determine the modal lifetimes of the components.**

**The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.**

Calculate the mode.

Run Scored | Number of Batsman |
---|---|

3000-4000 | 4 |

4000-5000 | 18 |

5000-6000 | 9 |

6000-7000 | 7 |

7000-8000 | 6 |

8000-9000 | 3 |

9000-10000 | 1 |

10000-11000 | 1 |

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

No of Students per teacher | Number of states / U.T |
---|---|

15-20 | 3 |

20-25 | 8 |

25-30 | 9 |

30-35 | 10 |

35-40 | 3 |

40-45 | 0 |

45-50 | 0 |

50-55 | 2 |

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

No. of Students per teacher | No. of states / U.T |
---|---|

15-20 | 3 |

20-25 | 8 |

25-30 | 9 |

30-35 | 10 |

35-40 | 3 |

40-45 | 0 |

45-50 | 0 |

50-55 | 2 |

Questions in Statistics - Exercise 14.3

**The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median.**

Monthly consumption(in units) | No. of customers |
---|---|

65-85 | 4 |

85-105 | 5 |

105-125 | 13 |

125-145 | 20 |

145-165 | 14 |

165-185 | 8 |

185-205 | 4 |

**The following frequency distribution gives the monthly consumption of electricity of 68 consumers in a locality. Find the mode.**

Monthly consumption(in units) | No. of customers |
---|---|

65-85 | 4 |

85-105 | 5 |

105-125 | 13 |

125-145 | 20 |

145-165 | 14 |

165-185 | 8 |

185-205 | 4 |

**The following frequency distribution gives the monthly consumption of electricity of 68 consumers in a locality. Find the mean by the step deviation method.

Monthly consumption(in units) | No. of customers |
---|---|

65-85 | 4 |

85-105 | 5 |

105-125 | 13 |

125-145 | 20 |

145-165 | 14 |

165-185 | 8 |

185-205 | 4 |

**The following table gives the distribution of a life time of 400 neon lamps.**

Lifetime (in hours) | Number of lamps |
---|---|

1500-2000 | 14 |

2000-2500 | 56 |

2500-3000 | 60 |

3000-3500 | 86 |

3500-4000 | 74 |

4000-4500 | 62 |

4500-5000 | 48 |

**Find the median lifetime of a lamp.**

**In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:**

Number of letters | 1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |
---|---|---|---|---|---|---|

Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |

**Determine the number of median letters in the surnames.**

**In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:**

Number of letters | 1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |
---|---|---|---|---|---|---|

Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |

**Find the number of mean letters in the surnames.**

**The distributions of below give a weight of 30 students of a class. Find the median weight of a student.**

Weight(in kg) | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 |
---|---|---|---|---|---|---|---|

Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |

**In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:**

Number of letters | 1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |
---|---|---|---|---|---|---|

Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |

**Find the size of modal in the surnames.**

**If the median of a distribution given below is 28.5 then, find the value of x & y.**

Class Interval | Frequency |
---|---|

0-10 | 5 |

10-20 | x |

20-30 | 20 |

30-40 | 15 |

40-50 | y |

50-60 | 5 |

Total | 60 |

Questions in Statistics - Exercise 14.4

**During the medical check-up of 35 students of a class, their weights were recorded as follows:**

Weight in kg | Number of students |
---|---|

Less than 38 | 0 |

Less than 40 | 3 |

Less than 42 | 5 |

Less than 44 | 9 |

Less than 46 | 14 |

Less than 48 | 28 |

Less than 50 | 32 |

Less than 52 | 35 |

**Find the median.**

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