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

Access detailed explanations (illustrated with images and videos) to 164 questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. Unlimited Access, Unlimited Time, on Unlimited Devices!

View Sample Explanation or View Features.

Rs. 550.00 -OR-

## Question 1

Measures of Location
Edit

Appeared in Year: 2010

### Describe in Detail

Essay▾

A cyclist pedals from his house to his college at a speed of 10 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 10 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 harmonic mean because it is suitable when the values are pertaining to the rate of change per unit time such…

… (9 more words) …

## Question 2

Measures of Location

Appeared in Year: 2010

### Describe in Detail

Essay▾

Let Fn (x) be the distribution function define by

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

### Explanation

The function Fn (x) is a distribution function if

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

## Question 3

Measures of Location

Appeared in Year: 2011

### Describe in Detail

Essay▾

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

a random variable with p. d. f. then σzα + 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

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

Assume

Then the limit is

Lower limit is - and upper limit is

If z = then the integral is same for given z and the quantile is

So, the quantile of X is .

## Question 4

Measures of Location
Edit

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 x1 , x2 , … , xn are n observations in a set have frequency f1 , f2, … , fn and the mean of observation is , then

Assume

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

… (16 more words) …

## Question 5

Measures of Location

Appeared in Year: 2015

### Describe in Detail

Essay▾

Let X have the probability density function

Find the mean, geometric mean and harmonic mean.

### Explanation

Then mean is

The geometric mean is

The geometric mean is

The harmonic mean is

## Question 6

Measures of Location
Edit

Appeared in Year: 2013

### Describe in Detail

Essay▾

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

### Explanation

If x1 , x2 , … , xn are the values having weights w1 , w2 , … , wn respectively, the weight mean is

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

… (5 more words) …

## Question 7

Measures of Location

Appeared in Year: 2013

### Describe in Detail

Essay▾

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 18 150 + x + y

Median is 46 which lies in the class 40 - 50. So, median class is 40 - 50.

Here n = 229, l = lower limit of median class = 40

cf = cumulative frequency of the above median class = 1…

… (39 more words) …

Developed by: