This document provides information about statistics concepts including measures of central tendency (mean, median, mode), calculating mean and median for grouped and ungrouped data, frequency distributions, and ogives. It also includes 50 multiple choice questions testing understanding of these statistical concepts. Key topics covered are calculating and comparing means, medians, and modes, determining class boundaries and mid-values, and identifying appropriate measures and formulas for grouped and ungrouped data sets.

1. 14. Statistics

2. 14. Statistics
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Statistics
1. The Mean for grouped data is calculated by
i. The direct method:
ii. The assumed mean method:
iii. The step deviation method:
2. The Mode for grouped data can be found formed by using the formula
Mode =
3. The Median for grouped data can be found formed by using the formula
Median=
4. While drawing Ogives , class boundaries are taken on -axis and corresponding
cumulative frequencies are taken on -axis
5. The median of grouped data can be obtained graphically as the coordinate of the
point of intersection of the two Ogives of the data.
6. Mode: A mode is that value among the observations which occurs most frequently.
7. If “n” is odd the Median is observation and if “n” is even then the Median will
be average of the and observations.
8. The Mean is the most frequently used measure of central tendency because it takes
into account all the observations, and lies between the extremes i.e., the largest and
the smallest observations of the entire data.

3. 14. Statistics
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Multiple choice Questions
1. If the arithmetic mean of then
(a) 1 (b)2 (c)3 (d)4
2. If the mean of first “n” natural numbers then
(a) 5 (b)4 (c)9 (d)10
3. Find the mean of the following distribution
Variable 4 6 9 10 15
frequency 5 10 10 7 8
(a) 4 (b)9 (c)6 (d)8
4. If the mean of the following distribution is 6 find the value of
Variable 2 4 6 10
frequency 3 2 3 1 2
(a) 4 (b)9 (c)6 (d)8
5. Calculate the median from the following distribution
Class
Interval
5-10 10-15 15-20 20-25 25-30 30-35 35-40
frequency 5 6 15 10 5 4 2
(a) 19.5 (b)16.5 (c)20.5 (d)17.5
6. The following are the marks of 9 students in a class. Find the median,
34, 32, 48, 38, 24, 30, 27,21,35
(a) 34 (b)32 (c)30 (d)21
7. Find the mode of the data 120, 110, 130, 110, 120, 140, 130, 120,140, 120
(a) 110 (b)130 (c)120 (d)140
8. Find the value of if the mode of the following data is 25
15, 20, 25, 18, 14, 15, 25, 15, 18, 16, 20, 25, 20, , 18
(a) 15 (b)18 (c)16 (d)25
9. 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 28-32 32-36 36-40
frequency 5 7 9 17 12 10 6 3 1 0
(a) 24.56 (b)32.66 (c)40.6 (d)36.5

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10. What is the value of the median of the data using the graph in the following figure of
less than Ogive and more than Ogive
(a) 4 (b)2 (c)12 (d)18
11. Which of the following is not a measure of central tendency?
(a) Mean (b)Median
(c)Mode (d)standard deviation
12. Which of the following cannot be determined graphically?
(a) Mean (b)Median
(c)Mode (d)None of the above
13. If the mean of the data 64, 60, 48, 43, 48, 43. 34 is 43 then
(a) 44 (b)45 (c)46 (d)48
14. If the mean of the frequency distribution is 8.1 and
then
(a) 3 (b)4 (c)5 (d)6
15. The mean of first “n” odd natural numbers is then
(a) 9 (b)81 (c)27 (d)18
16. Range of the values 20, 18, 37, 42, 3, 15, 15, 26 is
(a) 20 (b)40 (c)6 (d)39
17. A Histogram consists of
(a) Sectors (b)Rectangles (c)circles (d)squares
18. The width of a rectangle in a Histogram represents
(a) Mid value of the class (b)Class interval
(c)Frequency of the class (d)Number of classes

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19. In the frequency distribution with the classes 1-10, 11- ……. The upper boundary
of class 1-10 is
(a) 9.5 (b)42 (c)10.5 (d)10
20. Mid value of the class 1-10 is
(a) 5.5 (b)5 (c)11 (d)10
21. Median of observations . is
(a) (b) (c) (d)
22. If the number of observations in data is 17 then the median is ______ observation.
(a) 18th (b)7th (c)9th (d)6th
23. Median of is 4 then
(a) 16 (b)20 (c)12 (d)18
24. Arithmetic Mean of first natural numbers is
(a) (b) (c) (d)
25. Range of first natural numbers is
(a) (b) (c) (d)
26. Sum of the central angles in pie chart is
(a) (b) (c) (d)
27. If 1-8, 9-16, 17- 4……. are the classes of a frequency distribution the class interval is
(a) 16 (b)7 (c)9 (d)8
28. ________ is the most common and widely used measure of central tendency
(a) Arithmetic Mean (b)Median
(c)Mode (d)none
29. Range of first 100 natural numbers is ______
(a) 66 (b)98 (c)97 (d)99
30. The sum of 15 observations is 420 then Mean=
(a) 27 (b)28 (c)20 (d)16

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31. The mean of first “n” natural numbers
(a) (b) (c) (d)
32. Mode is denoted by the letter_______
(a) K (b)L (c)C (d)Z
33. The formula for the mean of ungrouped data is
(a) (b) (c) (d)
34. The mid value of the class is used to calculate for
(a) Arithmetic Mean (b)Median
(c)Mode (d)none
35. Formula for grouped data of the median
(a) (b)
(c) (d)none
36. The Arithmetic Mean of is
(a) (b) (c)3 (d)
37. The observation which occurs more frequently in a data
(a) Mode (b)Median
(c)Arithmetic Mean (d)none
38. The mode of data 2, 3, 3, 2, 3, 1 is then
(a) 1 (b)2 (c)3 (d)4
39. Most dependable average is
(a) Arithmetic Mean (b)Median
(c)Mode (d)none
40. Measure of central tendency
(a) 2 (b)3 (c)1 (d)4
41. Father of statistics is
(a) George Cantor (b)Sir Ronald-a- fisher
(c)Hipparcus (d)Archimedis

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42. 10-20, 20-30, 30-40, of the frequency distribution mid value of the 20-30
(a) 15 (b)25 (c)20 (d)none
43. _________ is not effected by extreme values
(a) Arithmetic Mean (b)Median
(c)Mode (d)none
44. Formula of Mode
(a) (b)
(c) (d)
45. Find the median of the daily wages of ten workers from the following data
Rupees 20, 25, 17, 18, 15, 22, 11, 9, 14
(a) 17 (b)25 (c)16 (d)8
46. The mean of 10 observations is 7 and the mean of 15 observations is 12. Then the
mean of all the observations is
(a) 7 (b)12 (c)10 (d)15
47. The mean of first five prime numbers is
(a) 5.6 (b)6.5 (c)3 (d)4
48. ________ is used in calculating arithmetic mean
(a) Greater than cumulative frequency
(b)less than cumulative frequency
(c)Mid values (d)none
49. The median of scores is 6 and then
(a) 6 (b)4 (c)2 (d)3
50. The arithmetic Mean of and is
(a) (b) (c) (d)

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Answers
1 2 3 4 5 6 7 8 9 10
d c b a a b c d b a
11 12 13 14 15 16 17 18 19 20
d a c d b d b b c a
21 22 23 24 25 26 27 28 29 30
b c c c a b d a d b
31 32 33 34 35 36 37 38 39 40
c d b a a a a c a b
41 42 43 44 45 46 47 48 49 50
b b b a c c a c d a