ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 45 - 49 of 164
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Question 45
Appeared in Year: 2010
Describe in Detail
Essay▾Show that for any discrete distribution, standard deviation is not less than mean deviation from mean.
Explanation
Here, we show that standard deviation is greater than mean deviation from mean.
S. D. ⩾ mean deviation from mean
(S. D.) 2 ⩾ (mean deviation from mean) 2
Let x1 , x2 , … , xn are n observations in a set have frequency f1 , f2, … , fn and the mean of observation is , then
Assume
Which is essentially true as f1 , f2 , … are not negative. The equality ho…
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Question 46
Appeared in Year: 2014
Describe in Detail
Essay▾Consider two samples as follows:
Sample 1: 1, 4, 7, 9, 16, 17,22, 24
Sample 2: 2, 6, 10, 12, 18, 20, 26,28, 32
Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test. [Given value of Z for α = 0·05 = 1·645, where Z is N (0,1) ]
Explanation
Let the sample 1 consider the population X and sample 2 consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is
In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is
Sample: 1 2 4 6 7 9 10 12 16 17 18 20 22…
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Question 47
Appeared in Year: 2012
Describe in Detail
Essay▾Scores in a UPSC examination in Statistics Paper-I and Paper-II awarded to 10 candidates were as under:
Candidate | A | B | C | D | E | F | G | H | I | J |
Score in Paper- I | 91 | 65 | 80 | 120 | 80 | 140 | 105 | 80 | 42 | 72 |
Score in Paper-II | 86 | 38 | 75 | 135 | 85 | 135 | 94 | 101 | 45 | 65 |
Calculate Spearman՚s rank correlation coefficient between the scores in the two papers.
Explanation
The method of calculating the association between the ranks is known as Spearman՚s rank correlation. The candidates are rank by the UPSC examination taken for two papers which is independent. The Spearman՚s rank correlation is
where n is the number of candidates and di is the difference between the rank of the i th individual.
For this, we give the r…
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Question 48
Appeared in Year: 2010
Describe in Detail
Essay▾Let X have a geometric distribution, then for an two non-negative integers m and n,
Prove it
Explanation
This proof is a lack of memory property. We known that
Therefore … (1)
The equation is
Using equation (1)
Since the equation is true. Therefore,
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Question 49
Appeared in Year: 2013
Describe in Detail
Essay▾Evaluate the following by taking seven ordinates of the integrand:
Explanation
The seven ordinates of the integrand using Simpson՚s rule is
Where
Here,
Using Simpson՚s rule is
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