B.Sc. (STATISTICS)
SEMESTER -1
DESCRIPTIVE STATISTICS
(QUESTION BANK)
UNIT
-1:
Essay Questions
1.
Define
Statistics and discuss its scope.
2.
What
is Statistics? Explain the importance of statistics in different fields.
3.
Define
Primary and Secondary data. Explain various methods that are used in the
collection of primary data and pointing out their merits and demerits.
4.
Distinguish
between primary and secondary data.
5.
What
are the advantages of diagrammatic and graphic presentation of data?
6.
What
are the different methods of a graphical presentation of data? Explain them.
7.
Draw
histogram, frequency polygon, frequency curve and Ogive curves to the given
data.
|
Variable |
05-09 |
10-14 |
15-19 |
20-24 |
25-29 |
30-34 |
35-39 |
|
Frequency |
8 |
15 |
18 |
30 |
16 |
12 |
6 |
8.
What
do you mean by central tendency? What are desirable properties for an average?
9.
Discuss
various measures of Central Tendency and its merits and demerits.
10.
Compute mean, median, mode, geometric mean and
harmonic mean from the following data.
|
Marks |
10-19 |
20-29 |
30-39 |
40-49 |
50-59 |
60-69 |
70-79 |
|
No. of Students |
8 |
19 |
29 |
36 |
25 |
13 |
4 |
Short Answer Questions
1.
Explain
the importance of statistics.
2.
What
is Questionnaire?
3.
What
are the essential characteristics of good questionnaire?
4.
Explain
the sources of Secondary data.
5.
Distinguish
between questionnaire and schedule
6.
What
are the methods of collecting primary data?
7.
What
do you understand by central tendency?
8.
Compute
mean, median, mode, geometric mean and harmonic mean from the following data.
|
Height in inches |
58 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
68 |
70 |
|
No. of Persons |
4 |
6 |
5 |
10 |
20 |
22 |
24 |
6 |
2 |
1 |
Very Short Very Short Answer Questions Questions
1.
Define Questionnaire
2.
Define Statistics
3.
Define Secondary Data
4.
Define Primary Data
5.
What are Ogive curves?
6.
When do we use bar diagrams?
7.
What is histogram?
8.
State the empirical relationship between mean, median
and mode.
9.
State various measures of central tendency.
10.
Compute
mean, median, mode, geometric mean and harmonic mean from the following data.
335, 384, 407, 672, 522, 777, 753, 2488, 1490
Unit-2
Essay
Questions
1. Crucially
examine different methods of variation
2. Describe
various measures of dispersion along with their respective merits and demerits.
3. What
is dispersion? What are various measures of dispersion? Explain them fully.
4. What
do you understand by skewness and kurtosis? Point out their role in analyzing
frequency distribution.
5. Define
moments. Obtain inter relationship between central moments in terms of
non-central moments vice-versa.
6. What
is skewness and kurtosis? Give some suitable measures of skewness and kurtosis.
7. Determine
range, Q.D, M.D, S.D from the given data.
|
Wages per Day |
02-04 |
04-06 |
06-08 |
08-10 |
10-12 |
12-14 |
|
No. of workers |
9 |
12 |
18 |
16 |
8 |
7 |
8. Calculate
Bowley’s coefficient of skewness from the given data.
|
Marks |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
|
No. of Students |
14 |
25 |
36 |
11 |
14 |
9. Karl
Pearson’s coefficient of skewness of a distribution is 0.32, its sd is 6.5 and
mean is 29.6. Find the mode of the distribution.
10. In
a frequency distribution, the coefficient of skewness based upon the quartiles
is 0.6. If the sum of the upper and lower quartiles is 100 and median is 38.
Find the values of upper and lower quartiles.
Short
Answer Questions
1. State
different methods of measuring skewness
2. State
different methods of measuring kurtosis
3. What
are the good properties of dispersion?
4. Write
a note on “Sheppard corrections”
5. What
are relative measures of dispersion?
6. Describe
absolute measures of dispersion.
7. Show
that for any frequency distribution (i). kurtosis is greater than unity (ii).
coefficient of skewness is less than 1 numerically.
8. Obtain
the limits of Bowley’s coefficient of skewness.
9. First
three moments of distribution about the value 2 are 1, 16 and 40 respectively.
Examine the skewness of distribution.
10. Show
that Pearson’s beta coefficients satisfy the inequality β2-β1-1≥0
also deduce β2>1.
Very
Short Answer Questions
1. What
is skewness?
2. What
is kurtosis?
3. For
symmetric distribution, what is β1 value?
4. What
are measures of skewness?
5. What
is the formula for relative measure of Q.D?
6. What
is the formula for relative measure of S.D?
7. Mean
of 100 observations is 50 and S.D. is 10. What will the new mean and S.d if 5
is added to each observation.
8. What
is the relationship between mean, median and mode in symmetric distribution?
9. What
is the relationship between mean, median and mode in positively skewed
distribution?
10. What
is the relationship between mean, median and mode in positively skewed
distribution?
Unit-3
Essay
Questions
1. Describe
the method of fitting the following curves.
(i). Y=aebx (ii). Y=aXb
2. Explain
the method of least squares and Describe its applications in fitting of curve of
the form Y=a+bX
3. Fit
an exponential curve of the form Y=abX to the following data.
|
X |
2 |
3 |
4 |
5 |
6 |
|
Y |
144 |
172.8 |
207.4 |
248.8 |
298.6 |
4. For
the data given below, find the equation of to the best fitting exponential
curve of the form Y=aebx
|
X |
1 |
2 |
3 |
4 |
5 |
6 |
|
Y |
1.6 |
4.5 |
13.8 |
40.2 |
125 |
300 |
5. The
marks obtained by 10 students in Mathematics and Statistics are given below.
Find the coefficient of correlation between the two subjects.(Karl Pearson’s
& Spearmen method)
|
Marks
in Mathematics |
75 |
30 |
60 |
80 |
53 |
35 |
15 |
40 |
38 |
48 |
|
Marks
in Statistics |
85 |
45 |
54 |
91 |
58 |
63 |
35 |
43 |
45 |
44 |
6. From the following data, compute the coefficient of correlation between X and YFrom
|
|
X series |
Y series |
|
No.of
Items |
15 |
15 |
|
Arithmetic
Mean |
25 |
18 |
|
Sum
of squares of deviations from mean |
136 |
138 |
7. In
two sets of variables X and Y with 50 observations each of the following were
obtained:
mean of x = 10, sd of x = 3, mean of y = 6, sd of y = 2 and r(x, y) = 0.3
But on subsequent verification, it was found that one
value of x (=10) and the value of Y) =6) were inaccurate and hence weeded out.
With the remaining 49 pairs of values, how is the original value r affected?
8. Derive
the formula for rank correlation coefficient when the ranks are tied and not
tied.
Short
Answer Questions
1. Show
that the coefficient of correlation independent of change of origin and scale
of the variables.
2. Explain
about partial correlation
3. State
the properties of correlation coefficient
4. Derive
the limits of rank correlation coefficient
5. State
the properties of multiple correlation coefficients.
6. Explain
about the principle least squares.
7. Explain
about bi-variate frequency distribution.
8. Explain
about the Probable Error.
Very
Short Answer Questions
1. Define
scatter diagram
2. State
the limits of Karl Pearson correlation coefficient
3. Define
bi-variate frequency distribution.
4. Define
multiple correlations.
5. Define
partial correlation coefficient.
6. Formula
for Spearmen’s formula.
7. What
is r12.3 ?
8. What
is R1.23?
Unit-4
Essay
Questions
1. Explain
what are regression lines. Derive their equations.
2. Explain
the properties of regression coefficients.
3. Distinguish
between correlation and regression.
4. You
are given the following information about advertising expenditure and sales:
|
|
Advt.
Exp (X) |
Sales
(Y) |
|
|
(Rs.In
Lakhs) |
(Rs.In
Lakhs) |
|
Mean |
10 |
90 |
|
S.D |
3 |
12 |
|
Correlation coefficient = 0.8 |
||
What should be the advertising budget if the company
wants to attain sales target of Rs. 120 lakhs?
5. The
equations of two regression lines: 3X+12Y=19, 3Y+9X=46. Obtain the value of (i).
Correlation coefficient and (ii). mean values of X and Y.
Short
Answer Questions
1. Explain
the concept of regression.
2. Show
that regression coefficients are independent of change of origin but not scale.
3. Obtain
the angle between two regression equations.
4. If
the two regression lines are given as x+2y-5=0 and 2x+3y=8, then find the mean
values of x and y.
5. Give
the interpretation for two cases r=0 and r=1
6. State
the standard error of estimate of for linear regression of y on x.
Very
Short Answer Questions
1. The
regression coefficients are b1 and b2 then, find
correlation coefficient.
2. Define
regression.
3. What
is the standard error of r?
4. Explain
why we have two regression lines.
5. State
Regression equation of y on x
6. State
Regression equation of x on y
Unit-5
Essay
Questions
1. What
do you mean by independence of attributes? Give a criterion of independence for
two attributes.
2. What
are the various methods of finding whether two attributes are associated,
disassociated or independent? Deduce any one such measure of association.
3. Derive
an expression for a measure of association between two attributes.
4. Define
Yule’s coefficient of association (Q) and coefficient of Colligation (Y).
Establish the relationship between them.
5. Find
whether attributes α and β are positively associated, negatively associated or
independent. Given (AB) =500, (α) = 800, (B) = 600, N = 1500.
6. ST
for n attributes A1, A2, . . . . ,An
(A1, A2, . . . . ,An)
≥ (A1) + (A2) + . . . . +(An) – (n-1)N
7. Briefly
explain the coefficient of contingency and its measures.
8. What
do you understand by consistency? How do you check it for three attributes?
9. A
student reported the results of a survey in the following manner, in terms of
usual notations
N=1000,
(A) = 525, (B) = 312, (C) = 470, (AB) = 42, (BC) = 86, (AC) = 147 and (ABC) =
25. Examine the consistency of given data.
Short
Answer Questions
1. When
two attributes are said to be positively associated and negatively associated.
2. What
is criterion for independence of two attributes?
3. What
are the conditions for consistency of two attributes?
4. Derive
the limits of coefficient of Colligation (Y)
5. Derive
the limits of coefficient of association (Q)
6. Explain
about manifold classification.
7. Given that (AB)/(B) > (Aβ)/ (β). Prove that (AB)/(A) > ( αB)/(α)
Very
Short Answer Questions
1. What
do you mean by order and order of class frequency?
2. Define
Classes and class frequencies.
3. Define
positive class frequencies.
4. Define
negative class frequencies
5. Examples
of attribute.
6. How
many total no. of class frequencies of all order for n attributes?
7. Define
ultimate classes
8. Define
ultimate class frequencies.
9. What
is the relationship between Yule’s coefficient of association (Q) and
coefficient of Colligation (Y).
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