ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 45 - 49 of 164

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Question 45

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Appeared in Year: 2010

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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

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Appeared in Year: 2014

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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

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Essay▾

Scores in a UPSC examination in Statistics Paper-I and Paper-II awarded to 10 candidates were as under:

Calculate Spearman՚S Rank Correlation Coefficient between the Scores in the Two Papers
CandidateABCDEFGHIJ
Score in Paper- I91658012080140105804272
Score in

Paper-II

86387513585135941014565

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

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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

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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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