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1

Calculate the mean for the following distribution:

x : | 5 | 6 | 7 | 8 | 9 |

y : | 4 | 8 | 14 | 11 | 3 |

2

Find the mean of the following data:

x: | 19 | 21 | 23 | 25 | 27 | 29 | 31 |

y: | 13 | 15 | 16 | 18 | 16 | 15 | 13 |

3

If the mean of the following data is 20.6. Find the value of p.

x: | 10 | 15 | p | 25 | 35 |

y: | 3 | 10 | 25 | 7 | 5 |

4

If the mean of the following data is 15, find p.

x : | 5 | 10 | 15 | 20 | 25 |

y : | 6 | p | 6 | 10 | 5 |

5

Find the value of p for the following distribution whose mean is 16.6

x : | 8 | 12 | 15 | p | 20 | 25 | 30 |

y : | 12 | 16 | 20 | 24 | 16 | 8 | 4 |

6

Find the missing value of p for the following distribution whose mean is 12.58

x: | 5 | 8 | 10 | 12 | p | 20 | 25 |

y: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |

7

Find the missing frequency (p) for the following distribution whose mean is 7.68.

x: | 3 | 5 | 7 | 9 | 11 | 13 |

y: | 6 | 8 | 15 | p | 8 | 4 |

8

Find the value of p, if the mean of the following distribution is 20.

x: | 15 | 17 | 19 | 20+p | 23 |

y: | 2 | 3 | 4 | 5p | 6 |

9

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students.

Age (in year): | 15 | 16 | 17 | 18 | 19 | 20 |

No. of students: | 3 | 8 | 10 | 10 | 5 | 4 |

10

Candidates of four schools appear in a mathematics test. The data were as follows:

Schools | No. of Candidates | Average Score |

I | 60 | 75 |

II | 48 | 80 |

III | Not available | 55 |

IV | 40 | 50 |

If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.

11

Five coins were simultaneously tossed 1000 times and at each toss the numbers of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss | No. of tosses |

0 | 38 |

1 | 144 |

2 | 342 |

3 | 287 |

4 | 164 |

5 | 25 |

Total | 1000 |

13

The arithmetic mean of the following data is 14. Find the value of k.

x | 5 | 10 | 15 | 20 | 25 |

y | 7 | k | 8 | 4 | 5 |

14

The arithmetic mean of the following data is 25, find the value of k.

x | 5 | 15 | 25 | 35 | 45 |

y | 3 | k | 3 | 6 | 2 |

[CBSE 2001]

15

If the mean of the following data is 18.75. Find the value of p.

x | 10 | 15 | p | 25 | 30 |

y | 5 | 10 | 7 | 8 | 2 |

1

The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table.

No. of calls (x): | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

No. of intervals (f): | 15 | 24 | 29 | 46 | 54 | 43 | 39 |

Compute the mean number of calls per interval.

2

Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss

No. of heads pre toss(x): | 0 | 1 | 2 | 3 | 4 | 5 |

No. of tosses (f): | 38 | 144 | 342 | 287 | 164 | 25 |

3

The following table gives the number of branches and number of plants in the garden of a school.

No. of branches (x): | 2 | 3 | 4 | 5 | 6 |

No. of plants (f): | 49 | 43 | 57 | 38 | 13 |

4

The following table gives the number of children of 150 families in a village

No. of children (x): | 0 | 1 | 2 | 3 | 4 | 5 |

No. of families (f): | 10 | 21 | 55 | 42 | 15 | 7 |

Find the average number of children per family.

5

The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Marks (x): | 15 | 20 | 22 | 24 | 25 | 30 | 33 | 38 | 45 |

Frequency (f): | 5 | 8 | 11 | 20 | 23 | 18 | 13 | 3 | 1 |

Find the average number of marks.

6

The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:

No. of students absent (x): | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

No. of days (f): | 1 | 4 | 10 | 50 | 34 | 15 | 4 | 2 |

Find the mean number of students absent per day.

7

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:

No. of misprints per pages (x): | 0 | 1 | 2 | 3 | 4 | 5 |

No. of pages (f): | 154 | 95 | 36 | 9 | 5 | 1 |

Find the average number of misprints per page.

8

The following distribution gives the number of accidents met by 160 workers in a factory during a month.

No. of accidents (x): | 0 | 1 | 2 | 3 | 4 |

No. of workers (f): | 70 | 52 | 34 | 3 | 1 |

Find the average number of accidents per worker.

9

Find the mean from the following frequency distribution of marks at a test in statistics:

Marks (x): | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

No. of students (f): | 15 | 50 | 80 | 76 | 72 | 45 | 39 | 9 | 8 | 6 |

1

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.

Expenditure (in rupees) (in rupees) | Frequency (f) | Expenditure (in rupees) (x) | Frequency (f) |

100-150 | 24 | 300-350 | 30 |

150-200 | 40 | 350-400 | 22 |

200-250 | 33 | 400-450 | 16 |

250-300 | 28 | 450-500 | 7 |

Find the average expenditure (in rupees) per household.

2

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.

Numbers of plants: | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |

Numbers of houses: | 1 | 2 | 1 | 5 | 6 | 2 | 3 |

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

3

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 |

Numbers of workers: | 12 | 14 | 8 | 6 | 10 |

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

4

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute recorded and summarized 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 |

Find the mean of each of the following frequency distributions: (5-14)

15

For the following distribution, calculate mean using all suitable methods:

Size of items: | 1-4 | 4-9 | 9-16 | 16-27 |

Frequency: | 6 | 12 | 26 | 20 |

16

The weekly observations on cost of living index in a certain city for the year 2004-2005 are given below. Compute the weekly cost of living index.

Cost of living Cost of living | Number of Students | Cost of living Index | Number of students |

1400-1500 | 3 | 1700-1800 | 9 |

1500-1600 | 10 | 1800-1900 | 6 |

1600-1700 | 20 | 1900-2000 | 2 |

17

The following table shows the marks scored by 140 students in an examination of a certain paper:

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

Number of students: | 20 | 24 | 40 | 36 | 20 |

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

18

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency is 50. Compute the missing frequency.

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

Frequency: | 5 | f1 | 10 | f2 | 7 | 8 |

19

The following distribution shows the daily pocket allowance given to the children of a multistory building. The average pocket allowance is Rs. 18.00. Find out the missing frequency.

Class interval: | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |

Frequency: | 7 | 6 | 9 | 13 | - | 5 | 4 |

20

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 |

21

In a retail market, fruit vendor 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?

22

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 |

23

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:

Concentration of SO | 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.

24

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.

Numbers 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 |

25

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 |

2

The following is the distribution of height of students of a certain class in a certain city.

Height (in cms): | 160-162 | 163-165 | 166-168 | 169-171 | 172-174 |

No. of students: | 15 | 118 | 142 | 127 | 18 |

Find the median height.

3

Following is the distribution of I.Q of 100 students. Find the median I.Q.

I.Q: | 55-64 | 65-74 | 75-84 | 85-94 | 95-104 | 105-114 | 115-124 | 125-134 | 135-144 |

No. of students: | 1 | 2 | 9 | 22 | 33 | 22 | 8 | 2 | 1 |

4

Calculate the median from the following data:

Rent (in Rs): | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 | 85-95 |

No. of Houses: | 8 | 10 | 15 | 25 | 40 | 20 | 15 | 7 |

5

Calculate the median from the following data:

Marks below: | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |

No. of students: | 15 | 35 | 60 | 84 | 96 | 127 | 198 | 250 |

6

An incomplete distribution is given as follows:

Variable: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

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

You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula fill up the missing frequency.

7

Calculate the missing frequency form 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 |

No. of persons: | 5 | 25 | ? | 18 | 7 |

8

Find the missing frequencies and the median for the following distribution if the mean is 1.46.

No. of accidents: | 0 | 1 | 2 | 3 | 4 | 5 | Total |

Frequency (No. of days): | 46 | ? | ? | 25 | 10 | 5 | 200 |

9

An incomplete distribution is given below:

Variable: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Frequency: | 12 | 30 | - | 65 | - | 25 | 18 |

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

10

The following table gives the frequency distribution of married women by age at marriage

Age (in years) | Frequency | Age (in years) | Frequency |

15-19 | 53 | 40-44 | 9 |

20-24 | 140 | 45-49 | 5 |

25-29 | 98 | 50-54 | 3 |

30-34 | 32 | 55-59 | 3 |

35-39 | 12 | 60 and above | 2 |

Calculate the median and interpret the results.

11

If the median of the following frequency distribution is 28.5 find the missing frequencies:

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

Total Frequency: | 5 | 20 | 15 | 5 | 60 |

12

The median of the following data is 525. Find he missing frequency, if it is given that there are 100 observations in the data:

Class Interval | Frequency | Class interval | Frequency |

0-100 | 2 | 500-600 | 20 |

100-200 | 5 | 600-700 | f |

200-300 | f | 700-800 | 9 |

300-400 | 12 | 800-900 | 7 |

400-500 | 17 | 900-1000 | 4 |

13

If the median of the following data is 32.5, find the missing frequencies.

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

Frequency: | f | 5 | 9 | 12 | f | 3 | 2 | 40 |

14

Compute the median for each of the following data

(i) Marks | No. of students | (ii) Marks | No. of students |

Less than 10 | 0 | More than150 | 0 |

Less than 30 | 10 | More than140 | 12 |

Less than 50 | 25 | More than130 | 27 |

Less than 70 | 43 | More than120 | 60 |

Less than 90 | 65 | More than110 | 105 |

Less than 110 | 87 | More than100 | 124 |

Less than 130 | 96 | More than90 | 141 |

Less than 150 | 100 | More than80 | 150 |

15

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm | Number of Girls |

Less than 140 | 4 |

Less than 145 | 11 |

Less than 150 | 29 |

Less than 155 | 40 |

Less than 160 | 46 |

Less than 165 | 51 |

Find the median height.

16

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 having age 18 years onwards but less than 60 years.

Age in years | Number of policy holders |

Blow 20 | 2 |

Blow 25 | 6 |

Blow 30 | 24 |

Blow 35 | 45 |

Blow 40 | 78 |

Blow 45 | 89 |

Blow 50 | 92 |

Blow 55 | 98 |

Blow 60 | 100 |

17

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

Length (in mm): | 118-126 | 127-135 | 136-144 | 14 5-153 | 154-162 | 163-171 | 172-180 |

No. of leaves: | 3 | 5 | 9 | 12 | 5 | 4 | 2 |

Find the median life.

18

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

Light time (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 life.

19

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

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

No. of students: | 2 | 3 | 8 | 6 | 6 | 3 | 2 |

2

The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:

Shirt size: | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 |

Number of persons: | 15 | 25 | 39 | 41 | 36 | 17 | 15 | 12 |

Find the model shirt size worn by the group.

3

Find the mode of the following distribution.

(i)

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

Frequency: | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |

(ii)

Class-interval: | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |

Frequency: | 30 | 45 | 75 | 35 | 25 | 15 |

(iii)

Class-interval: | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-60 |

Frequency: | 25 | 34 | 50 | 42 | 38 | 14 |

4

Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years): | 16-18 | 1-20 | 20-22 | 22-24 | 24-26 |

Group A: | 50 | 78 | 46 | 28 | 23 |

Group B: | 54 | 89 | 40 | 25 | 17 |

5

The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.

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

Frequency: | 3 | 5 | 16 | 12 | 13 | 20 | 5 | 4 | 1 | 1 |

6

The following is the distribution of height of students of certain class in a certain city:

Height (in cms): | 160-162 | 163-165 | 166-168 | 169-171 | 172-174 |

No. of students: | 15 | 118 | 142 | 127 | 18 |

Find the average height of maximum number of students.

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 |

No. of students: | 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.

8

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 |

No. of components: | 10 | 35 | 52 | 61 | 38 | 29 |

Determine the modal lifetimes of the components.

9

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 men monthly expenditure:

Expenditure (in Rs.) | 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 |

10

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 | 3 |

20-25 | 8 |

25-30 | 9 |

30-35 | 10 |

35-40 | 3 |

40-45 | 0 |

45-50 | 0 |

50-95 | 2 |

11

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 batsman |

3000-4000 | 4 |

4000-5000 | 18 |

5000-6000 | 9 |

6000-7000 | 7 |

7000-8000 | 6 |

8000-9000 | 3 |

9000-10000 | 1 |

10000-10000 | 1 |

Find the mode of the data.

12

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: | 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 |

13

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

Monthly consumption (in units): | 65-85 | 85-105 | 105-125 | 125-145 | 145-165 | 165-185 | 185-205 |

No. of consumers: | 4 | 5 | 13 | 20 | 14 | 8 | 4 |

14

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

Numbers of letters: | 1-4 | 4-7 | 7-10 | 10-13 | 13-16 | 16-19 |

Number 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.

15

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

Classes: | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |

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

16

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

Classes: | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |

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

17

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 |

1

Draw an ogive by less than method for the following data:

No. of rooms: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

No. of houses: | 4 | 9 | 22 | 28 | 24 | 12 | 8 | 6 | 5 | 2 |

2

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks | No. of Students |

600-400 | 16 |

640-680 | 45 |

680-720 | 156 |

720-760 | 284 |

760-800 | 172 |

800-840 | 59 |

840-880 | 18 |

Prepare a cumulative frequency table by less than method and draw an ogive.

3

Draw an ogive to represent the following frequency distribution:

Class-interval: | 0-4 | 5-9 | 10-14 | 15-19 | 20-24 |

No. of students: | 2 | 6 | 10 | 5 | 3 |

4

The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop: | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 |

No. of shops: | 12 | 18 | 27 | 20 | 17 | 6 |

Draw the frequency polygon for it.

5

The following table gives the height of trees:

Height | No. of trees |

Less than 7 | 26 |

Less than 14 | 57 |

Less than 21 | 92 |

Less than 28 | 134 |

Less than 35 | 216 |

Less than 42 | 287 |

Less than 49 | 341 |

Less than 56 | 360 |

Draw ‘less than’ ogive and ‘more than’ ogive.

6

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:

Profit (in lakhs in Rs.) | Number of shops (frequency) |

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 |

Draw both ogives for the above data and hence obtain the median.

7

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 above distribution to a less than type cumulative frequency distribution and draw its ogive.

8

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

Number of farms: | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 in kg per hectare |

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

Draw ‘less than’ ogive and ‘more than’ ogive.

9

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 |

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.

7

Write the modal class for the following frequency distribution:

Class-interval: | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |

Frequency: | 30 | 35 | 75 | 40 | 30 | 15 |

9

Write the median class for the following frequency distribution:

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

Frequency: | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |

12

Write the median class of the following distribution:

Classes: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

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

8

Mode is

11

If the mean of the following distribution is 2.6, then the value of y is

Variable (x): | 1 | 2 | 3 | 4 | 5 |

Frequency: | 4 | 5 | y | 1 | 2 |

34

If , then =