Vardaan Learning Institute

Chapter Practice Sheet: Statistics

Class: 10 (CBSE) Subject: Mathematics Max. Marks: 50
SECTION A: OBJECTIVE TYPE QUESTIONS (1 Mark Each)
1. The class mark of the class 10-25 is:
  1. 15
  2. 17.5
  3. 20
  4. 22.5
[1]
2. If the mean and median of a data are 12 and 15 respectively, then its mode is:
  1. 13.5
  2. 21
  3. 6
  4. 18
[1]
3. Which of the following cannot be determined graphically?
  1. Mean
  2. Median
  3. Mode
  4. None of these
[1]
4. For the following distribution:
Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9
The sum of lower limits of the median class and modal class is:
  1. 15
  2. 25
  3. 30
  4. 35
[1]
5. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its:
  1. Mean
  2. Median
  3. Mode
  4. All three
[1]
6. If $x_i$'s are the mid-points of the class intervals of grouped data, $f_i$'s are the corresponding frequencies and $\bar{x}$ is the mean, then $\sum(f_i x_i - \bar{x})$ is equal to:
  1. 0
  2. -1
  3. 1
  4. 2
[1]
7. In the formula $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$, for finding the mean of grouped data, $d_i$'s are deviations from a of:
  1. Lower limits of the classes
  2. Upper limits of the classes
  3. Mid-points of the classes
  4. Frequencies of the class marks
[1]
8. While computing mean of grouped data, we assume that the frequencies are:
  1. Evenly distributed over all the classes
  2. Centred at the classmarks of the classes
  3. Centred at the upper limits of the classes
  4. Centred at the lower limits of the classes
[1]
9. The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:
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 5 71 48 20
The number of athletes who completed the race in less than 14.6 seconds is:
  1. 11
  2. 71
  3. 82
  4. 130
[1]
10. Assertion (A): The mode of data 2, 3, 5, 2, 4, 3, 2, 1 is 2.
Reason (R): The observation that occurs most frequently is called Mode.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
[1]
SECTION B: SHORT ANSWER TYPE QUESTIONS (2 Marks Each)
11. Find the mean of the following data:
Class 0-10 10-20 20-30 30-40 40-50
Frequency 3 5 9 5 3
[2]
12. Find the mode of the following data:
Class 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 10 35 52 61 38 29
[2]
13. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy Rate (%) 45-55 55-65 65-75 75-85 85-95
Number of Cities 3 10 11 8 3
[2]
14. The arithmetic mean of the following frequency distribution is 50. Find the value of the missing frequency p.
Class 0-20 20-40 40-60 60-80 80-100
Frequency 17 p 32 24 19
[2]
SECTION C: SHORT ANSWER TYPE II QUESTIONS (3 Marks Each)
15. If the median of the distribution given below is 28.5, find the values of x and y.
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 Total
Frequency 5 x 20 15 y 5 60
[3]
16. 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.
Allowance (Rs) 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Children 7 6 9 13 f 5 4
[3]
17. Calculate the median height from the following data:
Height (cm) 135-140 140-145 145-150 150-155 155-160 160-165
Boys 4 12 18 28 24 14
[3]
18. The arithmetic mean of the following frequency distribution is 25. Find the value of p.
Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 18 15 p 6
[3]
19. Compute the mode for the following frequency distribution:
Size of items 0-4 4-8 8-12 12-16 16-20 20-24 24-28
Frequency 5 7 9 17 12 10 6
[3]
20. Convert the following cumulative frequency distribution into a standard frequency distribution:
Marks Below 10 Below 20 Below 30 Below 40 Below 50 Below 60
No. of Students 6 15 29 41 60 70
Also find the modal class.
[3]
SECTION D: LONG ANSWER TYPE QUESTIONS (5 Marks Each)
21. The following table gives the daily income of 50 workers of a factory:
Daily Income (Rs) 100-120 120-140 140-160 160-180 180-200
No. of Workers 12 14 8 6 10
Find the Mean, Median and Mode of the above data.
[5]
22. The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
Class Interval 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000
Frequency 2 5 x 12 17 20 y 9 7 4
[5]
SECTION E: CASE STUDY (4 Marks)
23. Case Study: COVID-19 Patients
A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data was obtained:
Height (in cm) Less than 140 Less than 145 Less than 150 Less than 155 Less than 160 Less than 165
Number of Girls 4 11 29 40 46 51
(i) Convert the above cumulative frequency distribution to a frequency distribution. (2 Marks)
(ii) Find the median height. (2 Marks)
[4]