Statistical Methods-Measures of Location (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 7 of 7

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Question number: 1

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

Describe in Detail

A cyclist pedals from his house to his college at a speed of l0 km per hour and back from the college to his house at 15 km per hour. Find the average speed.

Explanation

Given that a cyclist pedals from his house to his college at a speed of l0 km per hour and back from the college to his house at 15 km per hour. Assume that the distance between the house to college is d. Here the average speed is finding by

… (40 more words) …

Question number: 2

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let F n (x) be the distribution function define by

Equation

Is the lim F n (x) a distribution function? If not, why?

Explanation

The function F n (x) is a distribution function if

Equation

Equation

Equation

By the definition Equation , but here this is not equal to one. This says that F n (x) is not a distribution function.

Question number: 3

» Statistical Methods » Measures of Location

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Z be a random variable with p. d. f. f (z). Let z α be its upper α th quantile. Show that if X is

a random variable with p. d. f. Equation then σz α +µ is the upper α th quantile of X.

Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

Equation

X is a random variable with p. d. f. Equation , then quantile is

Equation

Assume Equation

Then the limit is

Lower limit is - Equation and upper

… (30 more words) …

Question number: 4

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

Describe in Detail

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

… (48 more words) …

Question number: 5

» Statistical Methods » Measures of Location

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X have the probability density function

Equation

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

The harmonic mean is

Equation

Equation

Equation

Equation

Question number: 6

» Statistical Methods » Measures of Location

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

Explanation

If x 1, x 2, …, x n are the values having weights w 1, w 2, …, w n respectively, the weight mean is

Equation

Here X is first ‘n’ natural numbers that is 1, 2, 3, …, n

Equation

Equation

Equation

Equation

Question number: 7

» Statistical Methods » Measures of Location

Appeared in Year: 2013

Essay Question▾

Describe in Detail

For the following frequency distribution on 229 values:

Class

Frequency

0 - 10

12

10 - 20

30

20 - 30

x

30 - 40

65

40 - 50

y

50 - 60

25

60 - 70

18

the median is found to be 46. Find the values of x and y.

Explanation

The cumulative frequency is

Class

Frequency

Cumulative frequency

0 - 10

12

12

10 - 20

30

42

20 - 30

x

42 + x

30 - 40

65

107 + x

40 - 50

y

107 + x+y

50 - 60

25

132 + x+y

60 - 70

18

… (107 more words) …

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