ADL 25 Statistics V1

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ADL 25 Statistics V1

Assignment – A
Question 1. Discuss the different types of bars and diagram’s used in statistics
for representation of data? Write the merits and limitations of each.
Question 2. How census survey is different from sample survey? Discuss the
different methods of sampling.
Question 3. Write short notes on the followings;
Absolute and Relative Measures of Dispersion
Importance of Index Numbers
Components of Time Series
Question 4. Following is an ogive comparing the rates of return for stocks A and
B

i. Use the ogive to estimate the number of years in which the average rate of
return for stock A exceeded 30%.
Assignment – B
Question 1. Grace Bros recently advertised a sale on ladies clothing. Fifty
customers were randomly selected and the amount spent at the sale was recorded.
These amounts are summarised below.

i. Use the statistics functions to estimate the mean and standard deviation
amount spent by the fifty customers.
ii. Your answers to part i. are only estimates. Explain why.
Question 2. The amount of petrol, which an estate agent used in driving
prospective buyers around the city to inspect home units, was recorded each week
for 200 weeks. The amounts were found to follow an approximate normal
distribution with a mean of 75 litres and standard deviation of 12 litres.
i. Find the probability the fuel consumption was more than 70 litres.
ii. Find the probability the fuel consumption was less than 60 litres.
iii. Estimate the number of weeks the fuel consumption was less than 60 litres.
iv. What fuel consumption was exceeded in only 20 out of the 200 weeks?
Question 3. (i) Find two regression lines with the help of following bivariate
distribution. Also comment on the value of R2:

(ii) Construct the fishers index number using the following data and show how it
Satisfies the time reversal tests.

CommodityBase QuantityBase PriceCurrent QuantityCurrent Price
A20123015
B13141520
C12102015
D86104
E5856

Case Study
RISK RETURN ANALYSIS: STOCK MARKET
You have just finished your management and degree and is appointed as trainee
with a equity research company. On the very first day of the job your boss Mr
Manshukh Mehta asked you to meet a client Mr Tapanlal and to understand his
requirements. Mr tapan lal is a big business and want to invest his savings into
stock market. But as he is not having any professional qualification so he is
not aware about the statistical analysis of risk and return. He does not want to
invest only on the basis of market news and rumors but want a deep investigation
with help of statistical analysis. He wants you to analyse some stocks and to
measure their risk and return. As you have already done a course of business
statistics and fully aware about the statistical analysis. You know very well
that you can use the concept of arithmetic mean and standard deviation for
calculating return and risk respectively. You can also calculate the correlation
of any stock with BSE SENSEX with help of correlation and regression analysis.
Following are the last six-month average monthly prices of five companies listed
on Bombay Stock exchange. (Return can be calculated by formula (Pn+1 – Pn)/ Pn)
MonthBSE
SENSEXTISCOJISCOSAILBSLISPAT
NOV’045432255435231127176
OCT’045132247412211145213
SEP’044256213435234165173
AUG’043891245489251211167
JULY’044325234471281291182
JUNE’044101213476251322189

Questions:
1. Calculate and compare monthly average return for each stock.
2. Calculate and compare risk of each stock.
3. Find the correlation of each stock with BSE SENSEX and comment on the
value.
Assignment – C
1. Which of the following is not a relative measure of dispersion?
(a) Standard deviation
(b) Range
(c) Coefficient of Variation
(d) Quartile Deviation
2. If coefficient of correlation between two variables is 0.6 than it means
(a) 60% of the variations between variables can be explained
(b) 6% of the variations between variables can be explained
(c) 36% of the variations between variables can be explained
(d) 16% of the variations between variables can be explained
3. Which of the following is an example of a population parameter?
(a). χ
(b). n
(c). μ
(d). s
(e). all of the above
4. When a distribution is symmetrical and has one mode, the highest point on the
curve is referred to as the
(a). range.
(b). mode
(c). median
(d). mean
(e). mode, median and mean, but not the range.
5. For a skewed distribution, the best measure of central tendency to report
(a). is the mean.
(b). is the median.
(c). is the range.
(d). depends on the direction of skewness
(e). is the mode.
6. The actual number of cups, which can be made from a sample of 20 different
brands of coffee makers, is given below.

11.0 10.5 9.0 11.0 8.5 8.5 8.5 10.5 9.5 9.0
11.5 10.5 11.0 9.0 9.5 11.0 9.5 11.0 9.0 10.5

The median number of cups from these coffee makers is
(a). 9.0
(b). 9.5
(c). 9.75
(d). 10.0
(e). 10.5
7. In a grouped frequency distribution the class intervals should be mutually
exclusive. This means that they should be
(A). of the same length.
(B). open ended.
(C). not open-ended.
(D). not overlapping
(E). none of the above.
8. The random variable “the number of STD phone calls made per month” is
(A). quantitative and discrete.
(B). quantitative and continuous
(C). qualitative and discrete
(D). qualitative and continuous
(E). categorical.
9. A coin is tossed five times. The probability of obtaining only one head in
five tosses is
(A). 1/64
(B). 1/32
(C). 1/16
(D). 5/16
(E). 5/32
Use the following information to answer questions 10, 11 and 12.
The owner of a restaurant is interested in studying the demand by patrons for
the Friday to Sunday weekend time period. Records were maintained that indicated
whether a dessert was ordered and the gender of the individual. The results were
as follows

Dessert ordered Male Female

Yes 96 40
No 224 240

A patron is selected at random.
10. Find the probability the patron will be male.
(A). 0.3
(B). 0.7
(C). 0.192
(D). 0.373
(E). 0.533
11 Find the probability the patron orders dessert and is female.
(A). 0.067
(B). 0.106
(C). 0.693
(D). 0.627
(E). 0.160
12. Find the probability the patron is a male, given he did not order dessert.
(A). 0.747
(B). 0.483
(C). 0.373
(D). 0.300
(E). 0.933
Use the following information to answer questions 13 and 14
In a clothing factory, the average number of machines that are inoperable on a
given day is three. Machine breakdowns occur randomly and independently.
13. What is the probability there will be six inoperable machines on any given
day?
(A). 0.966
(B). 0.050
(C). 0.986
(D). 0.028
(E). 0.077
14. What is the probability there will be less than 2 inoperable machines over
two days?
(A). 0.199
(B). 0.398
(C). 0.062
(D). 0.019
(E). 0.017
15. Z is the standard normal random variable. Find P(Z < 1.70)
(A). 0.3577
(B). 0.8577
(C). 0.4554
(D). 0.9554
(E). 0.0446
16. Which of the following is not the example of compressed data
(a) data array
(b) frequency distribution
(c) histogram
(d) ogive
17 If in a set of discrete value of observations, 50% values are greater than
25, then Q2 is:
(a) 20
(b) 25
(c) 50
(d) 75
18. If quartile deviation is 8 , then value of standard deviation is:
(a) 12
(b) 16
(c) 24
(d) None of these
19. Which of the following is least affected by extreme values of observations
in a data set
(a). range
(b). quartile deviation
(c). mean deviation
(d). standard deviation
20. The sum of squares of deviation from mean is:
(a) maximum
(b) minimum
(c) zero
(d) none of these
21. The number of classes in a frequency distribution depends on:
(a) size of the data set
(b) size of the population
(c) range of the observation
(d) all of these
22. Bayes theorem is useful in
(a) revising probability estimates
(b) computing conditional probabilities
(c) computing sequential probabilities
(d) none of above
23. What is the probability of getting more four in rolling a dice
(a) 1/6
(b) 1/3
(c) 1/2
(d) 1
24. If P(AB) = 0, then the events A and B are
(a) independent
(b) dependent
(c) equally likely
(d) None of these
25. If events are mutually exclusive, then
(a) Their probabilities are less than 1
(b) Their probabilities sum to one
(c) Both events can not occur at the same time
(d) Both the events contains every out come of the event
26. Two regression lines are perpendicular to each other when
(a) r = 0
(b) r = 0.3
(c) r = -0.5
(d) r = + (-) 1
27. Two regression coefficient are 0.8 and 0.2, then value of r is:
(a) 0.16
(b) – 0.16
(c) 0.40
(d) – 0.40
28. The standard error of estimate is a measure of:
(a) Closeness
(b) variability
(c) Linearity
(d) None of these
29. Forecasting time horizon includes
(a) Long range
(b) Medium range
(c) Short range
(d) All of the these
30. Consider the time series data for the quarters of 1995 and 1996. The third
quarter of 1996 would be coded as
(a) 2
(b) 3
(c) 5
(d) 6
31. A component of time series used for short term forecasting is
(a) trend
(b) seasonal
(c) cyclical
(d) irregular
32. The best average in the construction of then index number is
(a) median
(b) geometric mean
(c) mode
(d) arithmetic mean
33. The Paasche index number is based on
(a) base years quantities
(b) current years quantities
(c) average of base and current year
(d) None of the above
34. Fisher’s index number formula satisfies
(a) Circular test
(b) Factor reversal test
(c) Time reversal test
(d) Both b and c
35. The value of correlation coefficient
(a) depends on the origin
(b) depends on the units of scale
(c) depends on both a and b
(d) independent on a and b
36. A scatter diagram
(a) is a statistical test
(b) must be linear
(c) must be curvilinear
(d) is a graph of x and y
37. Which of the following is the non-random method of selecting samples from
the population
(a) Multistage sampling
(b) Cluster Sampling
(c) Quota Sampling
(d) All of the above
38. If mean and coefficient of variation of a data set is 10 and 5,
respectively, then the standard deviation is:
(a) 10
(b) 5
(c) 50
(d) none of the above
39. The standard deviation of a set of 50 observations is 6.5. If value of each
observation is increased by 5, then the standard deviation is:
(a) 2.5
(b) 1.5
(c) 3.5
(d) none of the above
40. The relationship between mean , median and mode is:
(a) Mean – median = 3(mean – mode)
(b) Mode = 3 median – 2 mean
(c) 3 median = 2 mean + mode
(d) All above

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