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Exercises in Chapter 6 statistics Grade 10

Questions in Statistics Exercise 7.1

Calculate the mean for the following distribution:

X: | 5 | 6 | 7 | 8 | 9 |

f: | 4 | 8 | 14 | 11 | 3 |

Find the mean of the following data:

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

f: | 13 | 15 | 16 | 18 | 16 | 15 | 13 |

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

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

f: | 3 | 10 | 25 | 7 | 5 |

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

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

f: | 6 | p | 6 | 10 | 5 |

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

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

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

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

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

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

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

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

f: | 6 | 8 | 15 | p | 8 | 4 |

Questions in Statistics Exercise 7.2

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.

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 |

Calculate the average number of branches per plant.

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.

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 per toss (x): | 0 | 1 | 2 | 3 | 4 | 5 |

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

Questions in Statistics Exercise 7.3

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

Expenditure (in rupees) (x) | Frequency (fi) | Expenditure (in rupees) (xi) | Frequency (fi) |
---|---|---|---|

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.

A survey was conducted by a group of students as a part of their environmental awareness program, in which they collected the following data regarding the number of plants in 200 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 house: | 1 | 2 | 1 | 5 | 6 | 2 | 3 |

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

Consider the following distribution of daily wages of workers of a factory

Daily wages (in ₹) | 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.

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)

Class interval: | 0 – 6 | 6 – 12 | 12 – 18 | 18 – 24 | 24 – 30 |

Frequency: | 6 | 8 | 10 | 9 | 7 |

Questions in Statistics Exercise 7.4

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

Life 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.

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 |

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

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

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

Find the median height.

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 |

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 |

Frequencies (no. of days): | 46 | ? | ? | 25 | 10 | 5 | 200 |

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 |

Calculate the median from the following data:

Marks below: | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 85 – 95 |

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

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 |

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

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 | 45 – 49 | 3 |

30 – 34 | 32 | 55 – 59 | 3 |

35 – 39 | 12 | 60 and above | 2 |

Calculate the median and interpret the results.

Questions in Statistics Exercise 7.5

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

Ages (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.

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.

The shirt size 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.

Find the mode of the following distribution.

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

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

Find the mode of the following distribution.

Class interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |

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

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

Age in years | 16 – 18 | 18 – 20 | 20 – 22 | 22 – 24 | 24 – 26 |

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

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

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

Heights(exclusive) | 160 – 162 | 163 – 165 | 166 – 168 | 169 – 171 | 172 – 174 |

Heights (inclusive) | 159.5 – 162.5 | 162.5 – 165.5 | 165.5 – 168.5 | 168.5 – 171.5 | 171.5 – 174.5 |

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

Find the average height of maximum number of students.

The following table gives the daily income of 50 workers of a factory:

Daily income | 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.

Find the mode of the following distribution.

Class interval | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 | 45 – 50 | 50 – 55 |

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

Questions in Statistics Exercise 7.6

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

Profit per shop | No of shops: |
---|---|

0 – 50 | 12 |

50 – 100 | 18 |

100 – 150 | 27 |

150 – 200 | 20 |

200 – 250 | 17 |

250 – 300 | 6 |

Draw the frequency polygon for it.

Draw an ogive by less than the 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 |

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

Marks | No. of Students |
---|---|

600 – 640 | 16 |

640 – 680 | 45 |

680 – 720 | 156 |

720 – 760 | 284 |

760 – 800 | 172 |

800 – 840 | 59 |

840 – 880 | 18 |

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

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 |

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

Daily income (in Rs): | No of workers: |
---|---|

100 – 120 | 12 |

120 – 140 | 14 |

140 – 160 | 8 |

160 – 180 | 6 |

180 – 200 | 10 |

Convert the above distribution to a ‘less than’ type cumulative frequency distribution and draw its ogive.

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