Brief Answer Questions:
[10 × 1 = 10]Distinguish between primary data and secondary data.
The following result were obtained:
Coefficient of variation=50%
SK(P)=0.5
S.D.=2
Find mean and mode.
The year of origin of the following straight line trend equation of profits (in lakhs of rupees) is 2008. Ŷ = 35 + 2X. Estimate the profit for the year 2015.
Calculate the average daily wages for the workers of two factories.
| Factory A | Factory B | |
| No. of wage earners | 80 | 20 |
| Average daily wages | Rs. 1560 | Rs. 1260 |
What will be the value of median of a moderately asymmetrical distribution, if the mean and mode are 30 and 24 respectively?
Calculate quartile deviation and coefficient of quartile deviation.
Q₁=62, Q₃=70
If n=50, ∑x=75, ∑y=80, ∑x²=130, ∑y²=140, ∑xy=120, find the value of r.
Find the trend line from the following data by semi-average method.
| Year | 2061 | 2062 | 2063 | 2064 | 2065 | 2066 |
| Sales | 22 | 26 | 24 | 27 | 26 | 28 |
Calculate the coefficient of variation of a distribution if mean is found to be 200 and variance of distribution is 36.
Find the median of the following data:
20, 15, 15, 22, 17, 28
Short Answer Questions: (Attempt any SIX Questions)
[6 × 5 = 30]What is sampling? Discuss various sampling techniques.
Draw less than ogive and more than ogive for the following data in a same plane and locate median.
| Height | 62-63 | 63-64 | 64-65 | 65-66 | 66-67 | 67-68 | 68-69 |
| Persons | 2 | 6 | 14 | 16 | 8 | 3 | 1 |
Compute the seasonal indices by the method of simple average for the following data.
| Quarter | 1988 | 1989 | 1990 | 1991 |
| I | 3.5 | 3.5 | 3.5 | 4.0 |
| II | 3.9 | 4.1 | 3.9 | 4.6 |
| III | 3.4 | 3.7 | 3.7 | 3.8 |
| IV | 3.6 | 4.8 | 4.0 | 4.5 |
Construct:
a) Five number summary
b) Box-and-whisker plot
70, 99, 88, 100, 120, 89, 99, 89, 98, 96, 114
A problem in Statistics is given to two students A and B whose chances of solving it are 1/3 and 1/4 respectively. Find the probability that
a) The problem will be solved.
b) Only one of them can solve the problem
c) None of them will solve the problem
Modal marks for a group of 47 students is 27. Five students got the marks between 0-10, 15 students got the marks between 20-30 and 7 students got the marks between 40-50. Find the number of students getting marks between 10-20 and 30-40, if the minimum marks in the test were 50.
Fit a straight line trend for the following data and predict the likely profit for 1987.
| Year | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 |
| Profit (in Rs. 000) | 59 | 62 | 61 | 65 | 67 | 65 | 69 |
Comprehensive Answer Questions: (Attempt any TWO Questions)
[2 × 10 = 20]A factory produces two types of electric motors A and B. In an experiment relating to their life, the following results were obtained.
| Life(in years) | Number of motors Model A | Model B |
| 0-2 | 1 | 5 |
| 2-4 | 9 | 7 |
| 4-6 | 22 | 11 |
| 6-8 | 11 | 19 |
| 8-10 | 8 | 9 |
a) Find which model of motor has uniformity of life? Give reason
b) Calculate the combined mean.
From the data give below, find:
a) Two regression equations
b) The coefficient of correlation between the marks in Math and Statistics.
c) The most likely marks in Statistics when marks in Math is 30.
| Marks in Math | 25 | 28 | 35 | 32 | 31 | 36 | 29 | 38 | 34 | 32 |
| Marks in Statistics | 43 | 46 | 49 | 41 | 36 | 32 | 31 | 30 | 33 | 39 |
From the following income distribution, find:
a) Lowest income of richest 10% of the people
b) Limits of income of middle 60% of the people
| Income | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| No. of persons | 10 | 30 | 36 | 30 | 14 |