Revision/test (Standard Deviation)

1) The standard deviation of 1,2,3, ...., n is √14. What is the value of n.

A) 11  B) 13   C) 12   D) 14

2) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.
A) 2.78  B) 1.58 C) 1.48  D) 2.58

3) Find the standard deviation: 49, 63, 46, 59, 65, 52, 60, 54
A) 36.7  B) 34.9 C) 26.4  D) 36.5

4) Find the standard deviation: 20, 85, 120, 60, 40.
A) 6.78  B) 6.36 C) 6.48  D) 6.38

5) Find the standard deviation: 4, 5, 6, 6, 7, 8
A) 2.78  B) 1.29 C) 1.48  D) 1.58

6) Find the standard deviation: 3, 5, 11, 7, 8, 10, 9, 12, 14, 11.
A) 3.78  B) 3.58 C) 3.48  D) 3.16

7) Find the standard deviation: 240.12, 240.13, 240.15, 240.12, 240.17, 240.15, 240.17, 249.16, 240.22, 240.21
A) 0.0785  B) 0.0585 C) 0.0325  D) 0.0352

8) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.10
A) 2.77  B) 2.87 C) 2.47  D) 2.57

9) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.10, 11
A) 3.76  B) 3.16 C) 3.46  D) 3.56

10) For a set of ungrouped values the following sums are found: N= 15, ∑x = 480, ∑x²= 15735. Find the standard deviation.
A) 3 B) 4 C) 5 D) 6

11) Calculate the variance of 1,5,6
A) 4.66 B) 4.86 C) 4.76 D) 4.96

12) Find the variance of the first n positive integers?
A) (n²-1)/12 B) 2(n²-1)/3 C) (n²- 3)/12 D) (n²-2)/12 

13) Find the standard deviation of:

X: 10    20    30    40   50    60

F:  9      18    25    27   14     7

A) 13.12 B) 13.56 C) 13.25 D) 13.52

14) Find the standard deviation of:

X: 25      36     45       55      65  
F: 60    130    150     130    30
A) 11.12 B) 11.56 C) 11.07 D) 11.52

15) Find the standard deviation of:
X: 50    55    60    65   70

F: 30    40    65    50   15   

A) 5.69 B) 5.49 C) 5.79 D)   5.59

16) Find the standard deviation of:
X: 30      40      50       60       70  
F: 64     132    153     140     51
A) 11.78 B) 11.64 C) 11.48 D) 11.58

17) Find the standard deviation of:
Height in inch   No.of students
59-61 61-63  63-65   65-67  67-69
F:  4      30        45        15        6
A) 1.58 B) 1.38 C) 1.85 D) 1.83

18) Find the standard deviation of:
X: 20-23   25-29   30-34   35-39
F:   16           28       14         12
A) 5.50 B) 13) 5.08 C) 5.05 D) 5.04

19) Find the standard deviation of:
Weight     No of students
120-124        12

125-129        25

130-134        28  

135-139       15

140-144       12

145-149        8

A) 7.58 B) 7.38 C) 7.18 D) 7.81

20) The mean of two samples of sizes 50 and 100 respectively are 54.4 and 50.3; and their SDs are 8 and 7 respectively. What is mean and SD of the combined set of observations?
A) 51.7, 7.6  B) 51.7, 7.8 C) 50.7, 7.6  D) 50.7, 7.8

21) The mean of two samples of sizes 15 and 22 respectively are 3.5 and 4.7 ; and their SDs are 3 and 4 respectively. What is mean and SD of the combined set of observations?
A) 4.21, 4.68 B) 3.21,3.68 C) 4.21, 3.68 D) 3.21, 4.68

22) The mean and SD of 20 samples is 10, and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Calculate the SD if the wrong item is replaced by 12.
A) 1.909  B) 1.099 C) 1.990 D) 1.900

23) The mean of two samples of sizes 10 were found to be 9.5 and 2.5 respectively. Later on an additional observation became available. This was 15, and it was included in the original sample. Find the SD of the 11 observations.
A) 2.68  B) 2.48 C) 2.84 D) 2.86

24) For a group containing 100 observations. The mean and SD are 8 and √10.5. For 50 observation selected from these 100 observations the mean and SD are 10 and 2 respectively. Find  mean and SD of the other half.
A) 6, 2  B) 5, 4 C) 6,3 D) 5,5

25) The mean of 20 samples is found to be 10, and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Calculate the SD if the wrong item is omitted.
A) 1.799  B) 1.997 C) 1.979 D) 1.907

26) The first of two samples has 100 items with mean 15 and SD 3. If the whole group has 250 items with mean 15.6 and SD √13.44. find the SD of the second group.
A) 3  B) 4 C) 5 D) 6

27) In a distribution of 200 boys, where 0-5, 5-10 etc. are groups, mean and SD are 40 and 15  respectively. On checking it was found that the marks obtained by one student was wrongly entered as 53 in place of 43. Find the correct SD.
A) 14.17 B) 14.77 C) 14.57 D) 14.97

28) A student obtained the mean and SD of 100 observations as  40 and 5.1 respectively. It was found later that he had wrongly copied one observation as 50, the correct figure being 40. Calculate the correct mean and SD.
A) 39.9, 5 B) 35.9, 9 C) 39.5, 9 D) 39.5, 5

29) Find the coefficient of variation: 40, 30, 80, 60, 50, 90, 70
A) 33.26 B) 33.33 C) 33.36 D) 33.44

30) Find the SD of
Marks(x)       No. Of students
00-10                  05
10-20                   10
20-30                   20
30-40                  40
40-50                  30
50-60                  20
60-70                  10
70-80                   4
A) 15.67 B) 15.65 C) 15.69 D) 15.63

31) Find the coefficient of variation
Marks(x)       No. Of students
01-10                  05
11-20                   12
21-30                   20
31-40                   25
41-50                  40
51-60                  22
61-70                  15
71-80                   6
81-90                   4
91-100                 1
A) 41.2 B) 45.2 C) 42.5 D) 52.4

32) Prices of a particular commodity in five years in two cities are given below:
Prices in City A           City B
  20                                  10
  22                                  20
  19                                  18
  23                                  12
  26                                  15
Find the City which had more stable prices.
A) A B) B C) both A and B D) N

33) Which factory has greater variability in industrial wages?
Factory-A  Average  SD employee
    A              34.5         5       476
    B              28.5        4.5    524
A) A B) B C) both A and B D) n