STANDARD DEVIATION
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1)Find S. D of
a)1,2,3,4,5,6,7,8,9
b) 46,63,46,59,52,60,54.
c) 20, 8,120,60,40.
d) 4,5,6,6,7,8
e) 3,5,11,7,8,10,9,12,14,11.
f) 240.12, 240.13, 240.15, 240.12, 240.17, 240.15, 249.17, 240.16, 240.22, 240.21.
g) 1,2,3,4,5,6,7,8,9,10
h) 1,2,3,4,5,6,7,8,9,10,11.
2) Calculate the variance of
a)1,5,6
b) first n positive integers ?
3) Find the coefficient of variation-
a)5,10,30,40,65
b) 40,30,80,60,50,90,70.
d) X: 1-10 11-20 21-30 31-40 41-50
F: 5 12 20 25 40
4) The S. D of 1,2,3…,n is√14 find n.
5) Find standard deviation of:
a) C. I: 2-4 4-6 6-8 8-10
F: 3. 4 2 1
b) X: 10 20 30 40 50 60
F:. 9 18 25 27 14 7
c) X: 25 36 45 55 65
F: 60 130 150 130 30
d) X: 50 55 60 65 70
F: 30 40 65 50 15
e) Age: 30 40 50 60 70
F:. 64 132 153 140 51
f) X: 59-61 61-63 63-65 65-67
F: 4 30 45 15
g) X: 20-24 25-29 30-34 35-39
F: 16 28 14 12
h) X: 120-124 125-129 130-134
F: 12 25 28
6) The mean of two samples of sizes 50 and 100 respectively are 54.4 and 50.3; and their SD are 8 and 7 . What is mean and SD of the combined set of observations?
7) A sample size 15 has mean 3.5, and SD is 3.0. another sample of size 22 has mean 4.7 and SD 4.0. If two samples are pooled together, find the mean and standard deviation of the combined sample.
8) The mean and SD of 20 items is found to be 10 and 2. 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.
9) The mean and SD of a sample size 10 were found to be 9.5 and 2.5. later on an additional observation become available. This was 15, and it was included in the original sample. Find the SD of the 11 observations.
10) For a group containing 100 observations, the mean and SD are 8 and√10.5. For 50 observations selected from those 100 observations the mean and SD are 10 and 2. Find the mean and SD of the other half.
11) The mean and SD of 20 items is found to be 10, and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Find the SD if the wrong item is omitted.
12) The first 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.
13) In a distribution of 200 boys, where 0-5,5-10 etc. are groups, mean and SD are 40 and 15. On checking it was found that the marks obtained by one student was wrongly taken as 53 in place of 43. Find the correct SD.
14) A student obtained the mean and SD of 100 observations as 40 and 5.1 respectively. It was later on found that he had wrongly copied one observation as 50, the correct figure being 40. Find correct mean, SD.
15) Prices of a particular commodity in five years in two cities are given:
City A: 20 22 19 23 26
City B: 10 20 18 12 15
Find the city which had more stable prices.
16) Which factory has greater variability in industrial wages ?
FACTORY: A B
SD: 34.5 28.5
EMPLOYEES: 476 524
17) The coefficient of variation for the two series are 58% and 69% respectively. Their Standard deviation are 21.2 and 15.6. compute their arithmetic means.
18) Wages paid last year to the cleaning and maintenance staff of a shopping mall had a mean of Rs30000 with a SD of Rs2400. What will be the new mean and SD if all wages are increased by
a)Rs 3000
b) 10%
19) The following facts were gathered regarding an industrial dispute:
Information Before After
No.of workers. 516 508
Mean wages. 49.50 51.75
Median Wages 52.70 50
Variance wages 100 121
Compare the position before and after the dispute in terms of modal wages and coefficient of variation.
19) The mean and SD of height reading of a group of a employees of a firm are found to be 172cm and 18cm, while the same measure for their weight reading are 65 kg and 9kg. Compare the variability of the height reading with that of the weight readings.
20) The performance of two batsman S and R in five successive one-day cricket matches are :
S: 32 48 71 05 40
R: 19 47 67 06 101
Identify the batsman who is more consistent.
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