1

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

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 |

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

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

3

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 Rs) | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |

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

4

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 for these women, choosing a suitable method

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

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

5

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. Which method of finding the mean did you choose?

6

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

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

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

Find the mean daily expenditure on food by a suitable method

7

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 SO | Frequency |

0.00 - 0.04 0.04 - 0.08 0.08 - 0.12 0.12 - 0.16 0.16 - 0.20 0.20 - 0.24 | 4 9 9 2 4 2 |

Find the mean concentration of SO_{2} in the air

8

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

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 |

9

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 - 95 |

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

1

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. Compare and interpret the two measures of central tendency

2

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

Lifetimes (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

3

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

Expenditure (in Rs) | Number of families |

1000 – 1500 1500 - 2000 2000 - 2500 2500 - 3000 3000 - 3500 3500 - 4000 4000 - 4500 4500 – 5000 | 24 40 33 28 30 22 16 7 |

4

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

Number of students per teacher | Number of states / U.T. |

15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 50 – 55 | 3 8 9 10 3 0 0 2 |

5

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

Runs scored | Number of batsmen |

3000 – 4000 4000 – 5000 5000 – 6000 6000 – 7000 7000 – 8000 8000 – 9000 9000 – 10000 10000 – 11000 | 4 18 9 7 6 3 1 1 |

Find the mode of the data

6

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

Number of cars | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60-70 | 70-80 |

Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |

1

The following frequency distribution gives the monthly consumption of electricity of68 consumers of a locality. Find the median, mean and mode of the data and compare them

Monthly consumption (in units) | Number of consumers |

65 – 85 85 - 105 105 - 125 125 - 145 145 - 165 165 - 185 185 – 205 | 4 5 13 20 14 8 4 |

2

If the median of the distribution given below is 28.5, find the values of x and y

Class interval | Frequency |

0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 | 5 X 20 15 y 5 |

Total | 60 |

3

A life insurance agent found the following data for distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to persons having age 18years onwards but less than 60 year

Age (in years) | Number of policy holders |

Below 20 Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 | 2 6 24 45 78 89 92 98 100 |

4

The lengths of 40 leaves of a plant are measured correct to the nearest milli meter, and the data obtained is represented in the following table:

Length (in mm) | Number of leaves |

118 - 126 127 - 135 136 - 144 145 - 153 154 - 162 163 - 171 172 - 180 | 3 5 9 12 5 4 2 |

Find the median length of the leaves

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5)

5

The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours) | Number of lamps |

1500 - 2000 2000 - 2500 2500 - 3000 3000 - 3500 3500 – 4000 4000 - 4500 4500 – 5000 | 14 56 60 86 74 62 48 |

Find the median life time of a lamp

6

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the 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 median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames

7

The distribution below gives the weights of 30 students of a class. Find the median weight of the students

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 |

1

The following distribution gives the daily income of 50 workers of a factory

Daily income (in Rs) | 100 - 120 | 120 - 140 | 140 - 160 | 160 – 180 | 180 - 200 |

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

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive

2

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 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52 | 0 3 5 9 14 28 32 35 |

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula

3

The following table gives production yield per hectare of wheat of 100 farms of a village

Production yield (in kh/ha) | 50 – 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |

Number of farms | 2 | 8 | 12 | 24 | 38 | 16 |

Change the distribution to a more than type distribution, and draw its ogive