Class 10 Mathematics (NCERT)

1. The empirical relationship between the three measures of central tendency is:

• A. 3 Median = Mode + 2 Mean
• B. Mode = 3 Mean - 2 Median
• C. Mean = 3 Median - 2 Mode
• D. 2 Median = Mode + 3 Mean

2. Class mark of a class interval is given by:

• A. Upper limit - Lower limit
• B. (Upper limit + Lower limit) / 2
• C. Upper limit / 2
• D. Lower limit / 2

3. For a frequency distribution, the mean is calculated using formula Σf_i x_i / Σf_i. This method is called:

• A. Assumed Mean Method
• B. Step-Deviation Method
• C. Direct Method
• D. Grouped Method

4. The mode of a grouped frequency distribution can be determined graphically from a:

• A. Histogram
• B. Frequency Polygon
• C. Ogive
• D. Pie Chart

5. The median of a grouped data can be found graphically by drawing:

• A. Histograms
• B. Ogives
• C. Bar graphs
• D. Pie charts

6. If mean = 20 and median = 22, then mode is equal to:

• A. 20
• B. 26
• C. 24
• D. 22

7. Sum of deviations of observations from their mean is always equal to:

• A. 0
• B. 1
• C. -1
• D. Mean

8. The class size of interval 10 - 25 is:

• A. 10
• B. 15
• C. 25
• D. 17.5

9. Which measure of central tendency is affected most by extreme values?

• A. Mean
• B. Median
• C. Mode
• D. Range

10. The mean of first 10 natural numbers is:

• A. 5
• B. 5.5
• C. 6
• D. 10

11. In the formula Mean = a + (Σf_i d_i / Σf_i), 'a' represents:

• A. Class size
• B. Assumed mean
• C. Frequency
• D. Cumulative frequency

12. Cumulative frequency table is useful in determining the:

• A. Mean
• B. Median
• C. Mode
• D. Range

13. The mode of the data 2, 3, 4, 3, 5, 3, 1, 2, 3, 4 is:

• A. 2
• B. 3
• C. 4
• D. 5

14. If the mode of a distribution is 8 and mean is 8, then median is:

• A. 8
• B. 16
• C. 24
• D. 4

15. The median of numbers 4, 1, 8, 3, 6, 9, 2 is:

• A. 3
• B. 4
• C. 6
• D. 5

16. Constructing a cumulative frequency table is useful in determining:

• A. Mean
• B. Median
• C. Mode
• D. All of these

17. While computing mean of grouped data, we assume that the frequencies are:

• A. Evenly distributed over all classes
• B. Centred at class marks of classes
• C. Concentrated at lower limits
• D. Concentrated at upper limits

18. If mean of x, x+3, x+6, x+9, and x+12 is 10, then x is:

• A. 1
• B. 2
• C. 3
• D. 4

19. In Step-Deviation Method, u_i is calculated as:

• A. (x_i - a) / h
• B. (a - x_i) / h
• C. h × (x_i - a)
• D. x_i - a

20. In modal class formula, f_1 represents:

• A. Frequency of modal class
• B. Frequency of class preceding modal class
• C. Frequency of class succeeding modal class
• D. Total frequency

21. The upper limit of modal class for data: [0-10: 5, 10-20: 8, 20-30: 12, 30-40: 6] is:

• A. 20
• B. 30
• C. 40
• D. 10

22. If the mean of first n natural numbers is 15, then n is equal to:

• A. 15
• B. 29
• C. 30
• D. 28

23. Which of the following is NOT a measure of central tendency?

• A. Mean
• B. Median
• C. Mode
• D. Standard Deviation

24. The mean of 5 observations is 12. If one observation is excluded, mean becomes 10. Excluded number is:

• A. 20
• B. 18
• C. 15
• D. 22

25. The algebraic sum of deviations of a set of n values from their mean is:

• A. n
• B. 0
• C. 1
• D. n/2

26. Median class is the class interval whose cumulative frequency is just greater than or equal to:

• A. N
• B. N / 2
• C. N / 4
• D. 2N

27. If each observation of a data set is multiplied by 3, its mean will:

• A. Remain same
• B. Become 3 times
• C. Increase by 3
• D. Become 1/3rd

28. For symmetrical distribution, relation between mean, median, and mode is:

• A. Mean = Median = Mode
• B. Mean > Median > Mode
• C. Mean < Median < Mode
• D. Mean + Mode = Median

29. What is the class mark of interval 40 - 50?

• A. 40
• B. 45
• C. 50
• D. 10

30. Point of intersection of 'less than' and 'more than' ogives corresponds to x-axis coordinate value of:

• A. Mean
• B. Median
• C. Mode
• D. Class size