# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 24 - 28 of 72

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## Question number: 24

» Statistical Methods » Measures of Location

Appeared in Year: 2010

### Describe in Detail

Show that for any discrete distribution, standard deviation is not less than mean deviation from mean.

### Explanation

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## Question number: 25

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2014

### Describe in Detail

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

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## Question number: 26

» Statistical Methods » Correlation Ratio

Appeared in Year: 2012

### Describe in Detail

Scores in a UPSC examination in Statistics Paper-I and Paper-II awarded to10 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

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## Question number: 27

» Statistical Methods » Order Statistics » Maximum

Appeared in Year: 2014

### Describe in Detail

Let X _{1}, X _{2}, …, X _{n} be n independently identically distributed random variables following an exponential distribution with mean parameter θ. Obtain the distributions of (i) Maximum (X _{1}, X _{2}, …, X _{n}); (ii) Minimum (X _{1}, X _{2}, …, X _{n}) and (iii) Median for n = 2m + 1, (m > 0)

### Explanation

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## Question number: 28

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2010

### Describe in Detail

The following data represent lifetimes (hours) of batteries for two different brands:

Brand A | 40 | 30 | 40 | 45 | 55 | 30 |

Brand B: | 50 | 50 | 45 | 55 | 60 | 40 |

Test whether two brands are the same.

### Explanation

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