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

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 , … , x_n are n observations in a set have frequency f₁ , f_2, … , f_n and the mean of observation is , then

Assume

Which is essentially true as f₁ , f₂ , … are not negative. The equality ho…

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…

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…

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,

The seven ordinates of the integrand using Simpson՚s rule is

Where

Here,

Using Simpson՚s rule is