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3

Compute the mean of the following data:

Class | 1 - 3 | 3 - 5 | 5 - 7 | 7 - 9 |

Frequency | 12 | 22 | 27 | 19 |

4

Find the mean, using direct method:

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

Frequency | 7 | 5 | 6 | 12 | 8 | 2 |

5

Calculate the mean of the following data, using direct method:

Class | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |

Frequency | 6 | 10 | 8 | 12 | 4 |

6

Compute the mean of the following data, using direct method:

Class | 0 - 100 | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 |

Frequency | 6 | 9 | 15 | 12 | 8 |

7

Using an appropriate method, find the mean of the following frequency distribution:

Class interval | 84 - 90 | 90 - 96 | 96 - 102 | 102 - 108 | 108 - 114 | 114 - 120 |

Frequency | 8 | 10 | 16 | 23 | 12 | 11 |

Which method did you use, and why?

8

If the mean of the following frequency distribution is 24, find the value of p.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Frequency | 3 | 4 | p | 3 | 2 |

9

The following distribution shows the daily pocket allowance of children of a locality. If 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 |

10

If the mean of the following frequency distribution is 54, find the value of p.

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

Frequency | 7 | p | 10 | 9 | 13 |

11

The mean of the following data is 42. Find the missing frequencies x and y if the Sum of frequencies is 100.

Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |

Frequency | 7 | 10 | x | 13 | y | 10 | 14 | 9 |

12

The daily expenditure of 100 families are given below. Calculate f_{1} and f_{2} if the mean daily expenditure is Rs.188.

Expenditure (in Rs.) | 140 - 160 | 160 - 180 | 180 - 200 | 200 - 220 | 220 - 240 |

Number of families | 5 | 25 | f | f | 5 |

13

The mean of the following frequency distribution is 57.6 and the Total number of observations is 50.

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |

Frequency | 7 | f | 12 | f | 8 | 5 |

Find f_{1} and f_{2}.

14

During a medical check - up, the number of heart beats per minute of 30 patients were recorded and Summarized as follows:

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

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

Find the mean heartbeats per minute for these patients, choosing a suitable method.

15

Find the mean marks per student, using Assumed - mean method:

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

Number of students | 12 | 18 | 27 | 20 | 17 | 6 |

16

Find the mean of the following frequency distribution, using the Assumed - mean method:

Class | 100 - 120 | 120 - 140 | 140 - 160 | 160 - 180 | 180 - 200 |

Frequency | 10 | 20 | 30 | 15 | 5 |

17

Find the mean of the following data, using the Assumed - mean method:

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |

Frequency | 20 | 35 | 52 | 44 | 38 | 31 |

18

The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method.

Literacy rate (%) | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 | 85 - 95 |

Number of cities | 4 | 11 | 12 | 9 | 4 |

19

Find the mean of the following frequency distribution using step - deviation method.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Frequency | 7 | 10 | 15 | 8 | 10 |

20

Find the mean of the following data, using step - deviation method:

Class | 5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |

Frequency | 6 | 10 | 16 | 15 | 24 | 8 | 7 |

21

The weights of tea in 70 packets are shown in the following table:

Weight (in grams) | 200 - 201 | 201 - 202 | 202 - 203 | 203 - 204 | 204 - 205 | 205 - 206 |

Number of packets | 13 | 27 | 18 | 10 | 1 | 1 |

Find the mean weight of packets using step - deviation method.

22

Find the mean of the following frequency distribution using a suitable method:

Class | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Frequency | 25 | 40 | 42 | 33 | 10 |

23

In an annual examination, marks (out of 90) obtained by students of Class X in mathematics are given below:

Marks obtained | 0 - 15 | 15 - 30 | 30 - 45 | 45 - 60 | 60 - 75 | 75 - 90 |

Number of students | 2 | 4 | 5 | 20 | 9 | 10 |

Find the mean marks.

24

Find the arithmetic mean of the following frequency distribution using step - deviation method:

Age (in years) | 18 - 24 | 24 - 30 | 30 - 36 | 36 - 42 | 42 - 48 | 48 - 54 |

Number of workers | 6 | 8 | 12 | 8 | 4 | 2 |

25

Find the mean of the following data using step - deviation method:

Class | 500 - 520 | 520 - 540 | 540 - 560 | 560 - 580 | 580 - 600 | 600 - 620 |

Frequency | 14 | 9 | 5 | 4 | 3 | 5 |

26

Find the mean age from the following frequency distribution:

Age (in years) | 25 - 29 | 30 - 34 | 35 - 39 | 40 - 44 | 45 - 49 | 50 - 54 | 55 - 59 |

Number of persons | 4 | 14 | 22 | 16 | 6 | 5 | 3 |

27

The following table shows the age distribution of patients of malaria in a village during a particular month:

Age (in years) | 5 - 14 | 15 - 24 | 25 - 34 | 35 - 44 | 45 - 54 | 55 - 64 |

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

Find the average age of the patients.

28

Weight of 60 eggs were recorded as given below:

Weight (in grams) | 75 - 79 | 80 - 84 | 85 - 89 | 90 - 94 | 95 - 99 | 100 - 104 | 105 - 109 |

Number of eggs | 4 | 9 | 13 | 17 | 12 | 3 | 2 |

Calculate their mean weight to the nearest gram.

29

The following table shows the marks scored by 80 students in an examination:

Marks | Less than 5 | Less than 10 | Less than 15 | Less than 20 | Less than 25 | Less than 30 | Less than 35 | Less than 40 |

Number of eggs | 3 | 10 | 25 | 49 | 65 | 73 | 78 | 80 |

Calculate the mean marks correct to 2 decimal places.

1

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.

Age (in years) | 0 - 15 | 15 - 30 | 30 - 45 | 45 - 60 | 60 - 75 |

Number of patients | 5 | 20 | 40 | 50 | 25 |

2

Compute the median from the following data:

Marks | 0 - 7 | 7 - 14 | 14 - 21 | 21 - 28 | 28 - 35 | 35 - 42 | 42 - 49 |

Number of students | 3 | 4 | 7 | 11 | 0 | 16 | 9 |

3

The following table shows the daily wages of workers in a factory:

Daily wages (in RS.) | 0 - 100 | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 |

Number of workers | 40 | 32 | 48 | 22 | 8 |

Find the median daily wage income of the workers.

4

Calculate the median from the following frequency distribution:

Class | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 |

Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 2 | 2 |

5

Given below is the number of units of electricity consumed in a week in a certain locality:

Consumption (in units) | 65 - 85 | 85 - 105 | 105 - 125 | 125 - 145 | 145 - 165 | 165 - 185 | 185 - 205 |

Number of consumers | 4 | 5 | 13 | 20 | 14 | 7 | 4 |

Calculate the median.

6

Calculate the median from the following data:

Height - (in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 |

No. of boys | 6 | 10 | 18 | 22 | 20 | 15 | 6 | 3 |

7

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Frequency | 5 | 25 | ? | 18 | 7 |

8

The median of the following data is 16. Find the missing frequencies a and b if the Total of frequencies is 70.

Class | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |

Frequency | 12 | A | 12 | 15 | b | 6 | 6 | 4 |

9

In the following data the median of the runs scored by 60 top batsmen of the world in one - day international cricket matches is 5000. Find the missing frequencies x and y.

Runs scored | 2500 - 3500 | 3500 - 4500 | 4500 - 5500 | 5500 - 6500 | 6500 - 7500 | 7500 - 8500 |

Number of batsmen | 5 | X | y | 12 | 6 | 2 |

10

If the median of the following frequency distribution is 32.5, find the values of f_{1} and f_{2}

Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | Total |

Number of batsmen | f | 5 | 9 | 12 | f | 3 | 2 | 40 |

11

Calculate the median for the following data:

Age (in years) | 19 - 25 | 26 - 32 | 33 - 39 | 40 - 46 | 47 - 53 | 54 - 60 |

Frequency | 35 | 96 | 68 | 102 | 35 | 4 |

12

Find the median wages for the following frequency distribution:

Wages per day (in Rs.) | 61 - 70 | 71 - 80 | 81 - 90 | 91 - 100 | 101 - 110 | 111 - 120 |

No. of women workers | 5 | 15 | 20 | 30 | 20 | 8 |

13

Find the median from the following data:

Class | 1 - 5 | 6 - 10 | 11 - 15 | 16 - 20 | 21 - 25 | 26 - 30 | 31 - 35 | 36 - 40 | 41 - 45 |

Frequency | 7 | 10 | 16 | 32 | 24 | 16 | 11 | 5 | 2 |

14

Find the median from the following data:

Marks | No. of students |

Below 10 | 12 |

Below 20 | 32 |

Below 30 | 57 |

Below 40 | 80 |

Below 50 | 92 |

Below 60 | 116 |

Below 70 | 164 |

Below 80 | 200 |

1

Find the mode of the following frequency distribution:

Marks | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

Number of students | 12 | 35 | 45 | 25 | 13 |

2

Compute the mode of the following data:

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

Frequency | 25 | 16 | 28 | 20 | 5 |

3

Heights of students of Class X are given in the following frequency distribution:

Height (in cm) | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 |

Number of students | 15 | 8 | 20 | 12 | 5 |

Find the modal height.

Also, find the mean height. Compare and interpret the two measures of central tendency.

4

Find the mode of the following distribution:

Class interval | 10 - 14 | 14 - 18 | 18 - 22 | 22 - 26 | 26 - 30 | 30 - 34 | 34 - 38 | 38 - 42 |

Frequency | 8 | 6 | 11 | 20 | 25 | 22 | 10 | 4 |

5

Given below is the distribution of Total household expenditure of 200 manual workers in a city.

Expenditure (in Rs.) | No of manual workers |

1000 - 1500 | 24 |

1500 - 2000 | 40 |

2000 - 2500 | 31 |

2500 - 3000 | 28 |

3000 - 3500 | 32 |

3500 - 4000 | 23 |

4000 - 4500 | 17 |

4500 - 5000 | 5 |

Find the expenditure done by maximum number of manual workers.

6

Calculate the mode from the following data:

Monthly salary (in Rs.) | No. of employees |

0 - 5000 | 90 |

5000 - 10000 | 150 |

10000 - 15000 | 100 |

15000 - 20000 | 80 |

20000 - 25000 | 70 |

25000 - 30000 | 10 |

7

Compute the mode from the following data:

Age (in years) | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 |

Number of patients | 6 | 11 | 18 | 24 | 17 | 13 | 5 |

8

Compute the mode from the following series:

Size | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 | 85 - 95 | 95 - 105 | 105 - 115 |

Frequency | 7 | 12 | 17 | 30 | 32 | 6 | 10 |

9

Compute the mode of the following data:

Class interval | 1 - 5 | 6 - 10 | 11 - 15 | 16 - 20 | 21 - 25 | 26 - 30 | 31 - 35 | 36 - 40 | 41 - 45 | 46 - 50 |

Frequency | 3 | 8 | 13 | 18 | 28 | 20 | 13 | 8 | 6 | 4 |

10

The agewise participation of students in the Annual Function of a school is shown in the following distribution.

Age (in years) | 5 - 7 | 7 - 9 | 9 - 11 | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 |

Number of students | x | 15 | 18 | 30 | 50 | 48 | X |

Find the missing frequencies when the Sum of frequencies is 181. Also, find the mode of the data.

1

Find the mean, mode and median of the following frequency distribution:

Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Number of batsmen | 4 | 4 | 7 | 10 | 12 | 8 | 5 |

2

Find the mean, median and mode of the following data:

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 | 120 - 140 |

Frequency | 6 | 8 | 10 | 12 | 6 | 5 | 3 |

3

Find the mean, median and mode of the following data:

Class | 0 - 50 | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 |

Frequency | 2 | 3 | 5 | 6 | 5 | 3 | 1 |

4

Find the mode, median and mean for the following data:

Marks obtained | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 |

Number of students | 7 | 31 | 33 | 17 | 11 | 1 |

5

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:

Height (in cm) | 120 - 130 | 130 - 140 | 140 - 150 | 150 - 160 | 160 - 170 | Total |

Total Number of girls | 2 | 8 | 12 | 20 | 8 | 50 |

Find the mean, median and mode of the above data.

6

The following table 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 |

Find the mean, mode and median of the above data.

7

The table below shows the daily expenditure on food of 30 households in a locality:

Daily expenditure (in Rs.) | Number of households |

100 - 150 | 6 |

150 - 200 | 7 |

200 - 250 | 12 |

250 - 300 | 3 |

300 - 350 | 2 |

Find the mean and median daily expenditure on food. [CBSE 2009C]

1

Find the median of the following data by making a 'less than ogive'.

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |

Number of students | 5 | 3 | 4 | 3 | 3 | 4 | 7 | 9 | 7 | 8 |

2

The given distribution shows the number of wickets taken by the bowlers in one - day international cricket matches:

Number of wickets | Less than 15 | Less than 30 | Less than 45 | Less than 60 | Less than 75 | Less than 90 | Less than 105 | Less than 120 |

Number of bowlers | 2 | 5 | 9 | 17 | 39 | 54 | 70 | 80 |

Draw a 'less than type' ogive from the above data. Find the median.

3

Draw a 'more than' ogive for the data given below which gives the marks of 100 students.

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |

Number of students | 4 | 6 | 10 | 10 | 25 | 22 | 18 | 5 |

4

The heights of 50 girls of Class X of a school are recorded as follows:

Height (in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 |

Number of girls | 5 | 8 | 9 | 12 | 14 | 2 |

Draw a 'more than type' ogive for the above data.

5

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly consumption (in units) | 140 - 160 | 160 - 180 | 180 - 200 | 200 - 220 | 220 - 240 | 240 - 260 | 260 - 280 |

Number of families | 3 | 8 | 15 | 40 | 50 | 30 | 10 |

Prepare a 'more than type' ogive for the given frequency distribution.

6

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

Production yield (kg/ha) | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |

Number of farms | 2 | 8 | 14 | 24 | 38 | 16 |

Change the distribution to a 'more than type' distribution and draw its ogive. Using ogive, find the median of the given data.

7

The table given below shows the weekly expenditures on food of some households in a locality.

Weekly expenditure (in Rs.) | Number of households |

100 - 200 | 5 |

200 - 300 | 6 |

300 - 400 | 11 |

400 - 500 | 13 |

500 - 600 | 5 |

600 - 700 | 4 |

700 - 800 | 3 |

800 - 900 | 2 |

Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

8

From the following frequency distribution, prepare the 'more than' ogive.

Score | Number of candidates |

400 - 450 | 20 |

450 - 500 | 35 |

500 - 550 | 40 |

550 - 600 | 32 |

600 - 650 | 24 |

650 - 700 | 27 |

700 - 750 | 18 |

750 - 800 | 34 |

Total | 230 |

Also, find the median.

9

The marks obtained by 100 students of a class in an examination are given below:

Marks | Number of students |

0 - 5 | 2 |

5 - 10 | 5 |

10 - 15 | 6 |

15 - 20 | 8 |

20 - 25 | 10 |

25 - 30 | 25 |

30 - 35 | 20 |

35 - 40 | 18 |

40 - 45 | 4 |

45 - 50 | 2 |

Draw cumulative frequency curves by using (i) 'less than' series and (ii) 'more than' series.

Hence, find the median.

10

From the following data, draw the two types of cumulative frequency curves and determine the median.

Height (in cm) | Frequency |

140 - 144 | 3 |

144 - 148 | 9 |

148 - 152 | 24 |

152 - 156 | 31 |

156 - 160 | 42 |

160 - 164 | 64 |

164 - 168 | 75 |

168 - 172 | 82 |

172 - 176 | 86 |

176 - 180 | 34 |

1

Write the median class of the following distribution:

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Frequency | 4 | 4 | 8 | 10 | 12 | 8 | 4 |

2

What is the lower limit of the modal class of the following frequency distribution?

Age (in years) | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

60 Number of patients | 16 | 13 | 6 | 11 | 27 | 18 |

3

The monthly pocket money of 50 students of a class are given in the following distribution:

Monthly pocket money (in Rs.) | 0 - 50 | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 |

Number of students | 2 | 7 | 8 | 30 | 12 | 1 |

Find the modal class and also give class mark of the modal class.

6

In a class test, 50 students obtained marks as follows:

Marks obtained | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

Number of students | 4 | 6 | 25 | 10 | 5 |

Find the modal class and the median class.

8

While calculating the mean of a given data by the Assumed - mean method, the following values were obtained:

A = 25, = 110, = 50.

Find the mean.

14

What is the cumulative frequency of the modal class of the following distribution?

Class | 3 - 6 | 6 - 9 | 9 - 12 | 12 - 15 | 15 - 18 | 18 - 21 | 21 - 24 |

Frequency | 7 | 13 | 10 | 23 | 4 | 21 | 16 |

15

Find the mode of the given data:

Class interval | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 |

Frequency | 15 | 6 | 18 | 10 |

16

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

Age (in years) | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Number of patients | 60 | 42 | 55 | 70 | 53 | 20 |

Form a 'less than type' cumulative frequency distribution.

17

In the following data, find the values of p and q. Also, find the median class and modal class.

Class | Frequency (f) | cummulative frequency (cf) |

100 - 200 | 11 | 11 |

200 - 300 | 12 | P |

300 - 400 | 10 | 33 |

400 - 500 | Q | 46 |

500 - 600 | 20 | 66 |

600 - 700 | 14 | 80 |

18

The following frequency distribution gives the monthly consumption of electricity of 64 consumers of a locality.

Monthly consumption (in units) | 65 - 85 | 85 - 105 | 105 - 125 | 125 - 145 | 145 - 165 | 165 - 185 |

Number of consumers | 4 | 5 | 13 | 20 | 14 | 8 |

Form a 'more than type' cumulative frequency distribution.

19

The following table gives the life - time (in days) of 100 electric bulbs of a certain brand.

Life - time (in days) | Less than 50 | Less than 100 | Less than 150 | Less than 200 | Less than 250 | Less than 300 |

Number of bulbs | 7 | 21 | 52 | 79 | 91 | 100 |

From this table, construct the frequency distribution table.

20

The following table gives the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

Marks obtained (in per cent) | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 | 51 - 60 | 61 - 70 | 71 - 80 |

Number of students | 141 | 221 | 439 | 529 | 495 | 322 | 153 |

(a) Convert the given frequency distribution into the continuous form.

(b) Find the median class and write its class mark.

(c) Find the modal class and write its cumulative frequency.

21

If the mean of the following distribution is 27, find the value of p.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Frequency | 8 | P | 12 | 13 | 10 |

22

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age (in years) | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Number of persons | 5 | 25 | ? | 18 | 7 |

14

Consider the frequency distribution of the heights of 60 students of a class:

Height (in cm) | No of Students | Cumulative Frequency |

150 - 155 | 16 | 16 |

155 - 160 | 12 | 28 |

160 - 165 | 9 | 37 |

165 - 170 | 7 | 44 |

170 - 175 | 10 | 54 |

175 - 180 | 6 | 60 |

The Sum of the lower limit of the modal class and the upper limit of the median class is

15

Consider the following frequency distribution:

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |

Frequency | 3 | 9 | 15 | 30 | 18 | 5 |

The modal class is

16

Mode = ?

17

Median = ?

19

Look at the frequency distribution table given below:

Class interval | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |

Frequency | 8 | 12 | 20 | 10 |

The median of the above distribution is

20

Consider the following table:

Class interval | 10 - 14 | 14 - 18 | 18 - 22 | 22 - 26 | 26 - 30 |

Frequency | 5 | 11 | 16 | 25 | 19 |

The mode of the above data is

24

Look at the cumulative frequency distribution table given below:

Monthly income | Number of families |

More than Rs. 10000 | 100 |

More than Rs. 14000 | 85 |

More than Rs. 18000 | 69 |

More than Rs.20000 | 50 |

More than Rs. 25000 | 37 |

More than Rs. 30000 | 15 |

Number of families having income range 20000 to 25000 is

29

Match the following columns:

Column I | Column II |

(a) The most frequent value in a data is known as ……. | (p) standard deviation |

(b) Which of the following cannot be determined graphically out of mean, mode and median? | (q) median |

(c) An ogive is used to determine ……. | (r) mean |

(d) Out of mean, mode, median and standard deviation, which is not a measure of central tendency? | (s) mode |

The correct answer is:

30

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A) | Reason (R) |

If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148. | Mean, median and mode of a frequency distribution are related as: mode = 3 median - 2 mean. |

31

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A) | Reason (R) | ||||||||||||||

Consider the following frequency distribution:
The mode of the above data is 12.4. | The value of the variable which occurs most often is the mode. |

3

Consider the following distribution:

Class interval | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 |

Frequency | 10 | 15 | 12 | 20 | 9 |

The Sum of the lower limits of the median class and the modal class is

4

Consider the following frequency distribution:

Class interval | 0 - 5 | 6 - 11 | 12 - 17 | 18 - 23 | 24 - 29 |

Frequency | 13 | 10 | 15 | 8 | 11 |

The upper limit of the median class is

6

In the table given below, the times taken by 120 athletes to run a 100 - m - hurdle race are given.

Class | 13.8 - 14 | 14 - 14.2 | 14.2 - 14.4 | 14.4 - 14.6 | 14.6 - 14.8 | 14.8 - 15 |

Frequency | 2 | 4 | 15 | 54 | 25 | 20 |

Find the number of athletes who completed the race in less than 14.6 seconds.

7

Consider the following frequency distribution:

Class | 0 - 5 | 6 - 11 | 12 - 17 | 18 - 23 | 24 - 29 |

Frequency | 13 | 10 | 15 | 8 | 11 |

Find the upper limit of the median class.

8

The annual profits earned by 30 shops of a shopping complex in a locality are recorded in the table shown below:

Profit (in lakh Rs.) | Number of shops |

More than or equal to 5 | 30 |

More than or equal to 10 | 28 |

More than or equal to 15 | 16 |

More than or equal to 20 | 14 |

More than or equal to 25 | 10 |

More than or equal to 30 | 7 |

More than or equal to 35 | 3 |

If we draw the frequency distribution table for the above data, find the frequency corresponding to the class 20 - 25.

9

Find the mean of the following frequency distribution:

Class | 1 - 3 | 3 - 5 | 5 - 7 | 7 - 9 |

Frequency | 9 | 22 | 27 | 18 |

10

The maximum bowling speeds (in km/hr) of 33 players at a cricket coaching centre are given below:

Speed in km/hr | 85 - 100 | 100 - 115 | 115 - 130 | 130 - 145 |

No. of players | 10 | 4 | 7 | 9 |

Calculate the median bowling speed.

11

The arithmetic mean of the following frequency distribution is 50.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Frequency | 16 | p | 30 | 32 | 14 |

Find the value of p.

12

Find the median of the following frequency distribution:

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

Number of students | 6 | 16 | 30 | 9 | 4 |

13

Following is the distribution of marks of 70 students in a periodical test:

Marks | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |

Number of students | 3 | 11 | 28 | 48 | 70 |

Draw a cumulative frequency curve for the above data.

14

Find the median of the following data.

Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | Total |

Number of students | 8 | 16 | 36 | 34 | 6 | 100 |

15

For the following distribution draw a 'less than type' ogive and from the curve find the median.

Marks obtained | Less than 20 | Less than 30 | Less than 40 | Less than 50 | Less than 60 | Less than 70 | Less than 80 | Less than 90 | Less than 100 |

Number of students | 2 | 7 | 17 | 40 | 60 | 82 | 85 | 90 | 100 |

16

The median value for the following frequency distribution is 35 and the Sum of all the frequencies is 170. Using the formula for median, find the missing frequencies.

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Frequency | 10 | 20 | ? | 40 | ? | 25 | 15 |

17

Find the missing frequencies f_{1} and f_{2} in the table given below, it being given that the mean of the given frequency distribution is 50.

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | Total |

Total Frequency | 17 | f | 32 | f | 19 | 120 |

18

Find the mean of the following frequency distribution using step - deviation method:

Class | 84 - 90 | 90 - 96 | 96 - 102 | 102 - 108 | 108 - 114 | 114 - 120 |

Frequency | 15 | 22 | 20 | 18 | 20 | 25 |

19

Find the mean, median and mode of the following data:

Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |

Frequency | 6 | 8 | 10 | 15 | 5 | 4 | 2 |

20

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data:

Class | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |

Frequency | 2 | 12 | 2 | 4 | 3 | 4 | 3 |

21

The production yield per hectare of wheat of some farms of a village are given in the following table:

Production yield (in kg/ha) | 40 - 45 | 45 - 50 | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 |

Number of farms | 1 | 9 | 15 | 18 | 40 | 26 | 16 | 14 | 10 |

Draw a less than type ogive and a more than type ogive for this data.

22

The following table gives the marks obtained by 50 students in a class test:

Marks | 11 - 15 | 16 - 20 | 21 - 25 | 26 - 30 | 31 - 35 | 36 - 40 | 41 - 45 | 46 - 50 |

Number of students | 2 | 3 | 6 | 4 | 14 | 12 | 4 | 2 |

Calculate the mean, median and mode for the above data.