Statistics MATHS - Statistics

 The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is:

1. 50,000
2. 250,000
3. 252500
4. 255000 

The standard deviation of first 10 natural numbers is:

1. 5.5
2. 3.87
3. 2.97
4. 2.87

Let x₁, x₂, ..., x_n be n observations. Let y_i = ax_i + by_i + b for i = 1, 2, 3, ..., n, where a and b are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of y_i's 55 and standard deviation of y_i's is 15, the values of a and b are:

1. a = 1.25, b = -5
2. a = -1.25, b = 5
3. a = 2.5, b = -5
4. a = 2.5, b = 5

If x₁, x₂, ..., x_n are n values of a variable X and y₁, y₂, ..., y_n are n values of variable Y such that y_i = ax_i + b, i = 1, 2, ..., n, then write Var(Y) in terms of Var(X).

If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.

If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.

In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to -k. If the standard deviation of the observations is 2, then write the value of k.

Find the mean variance and standard deviation for the following data:
2, 4, 5, 6, 8, 17.

Find the mean variance and standard deviation for the following data:
15, 22, 27, 11, 9, 21, 14, 9.

Two plants A and B of a factory show following results about the number of workers and the wages paid to them:

	Plant A	Plant B
No. of workers	5000	6000
Average monthly wages	₹ 2500	₹ 2500
Variance of distribution of wages	81	100

In which plant A or B is there greater variability in individual wages?

The means and standard deviations of heights ans weights of 50 students of a class are as follows:

	Weights	Heights
Mean	63.2kg	63.2 inch
Standard deviation	5.6kg	11.5 inch

Which shows more variability, heights or weights?

Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

Find the mean, and standard deviation for the following data:

Year render:	10	20	30	40	50	60
No. of persons(cumulative):	15	32	51	78	97	109

From the prices of shares X and Y given below: find out which is more stable in value:

x	35	54	52	53	56	58	52	50	51	49
y	108	107	105	105	106	107	104	103	104	101

Calculate the mean, variance and standard deviation of the following frequency distribution.

Class:	1-10	10-20	20-30	30-40	40-50	50-60
Frequency:	11	29	18	4	5	3

Find the standard deviation for the following distribution:

x	4.5	14.5	24.5	34.5	44.5	54.5	64.5
f	1	5	12	22	17	9	4