# 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 x_{1} , x_{2} , … , x_{n} are n observations in a set have frequency f_{1} , f_{2,} … , f_{n} and the mean of observation is , then

Assume

Which is essentially true as f_{1} , f_{2} , … 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 d_{i} 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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