# Statistical Methods-Dispersion and Skewness (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Statistical Methods » Dispersion and Skewness

Appeared in Year: 2012

### Describe in Detail

Show, by proving all intermediate results, that for a set of n unsorted data, the measure of skewness based on mean, median and standard deviation, necessarily lies between -3 and + 3.

### Explanation

The formula of measure of skewness given by Karl Pearson’s is

Also, we known the relation of mean, median and mode is

Mean-Mode = 3 (Mean-Median)

So,

Using Chebyshev’s inequality, X be a random variable with mean µ and variance σ ^{2} then any k > 0,

## Question number: 2

» Statistical Methods » Dispersion and Skewness

Appeared in Year: 2010

### Describe in Detail

The first three moments of a distribution about the value 1 are 2, 25 and 80. Find its mean standard deviation and the moment-measure of skewness.

### Explanation

Given that a = 1,

The mean is

The standard deviation is

Measure of skewness