Business Statistics Objective Set 3

1. Which of the following is not a relative measure of dispersion?

  1. Standard deviation[Ans]
  2. Range[Ans]
  3. Coefficient of Variation
  4. Quartile Deviation[Ans]

Note: Only the coefficient of variation is a relative measure of dispersion
2. If coefficient of correlation between two variables is 0.6 than it means

  1. 60% of the variations between variables can be explained[Ans]
  2. 6% of the variations between variables can be explained
  3. 36% of the variations between variables can be explained
  4. 16% of the variations between variables can be explained

3. Which of the following is an example of a population parameter?
a..
b. n

c. [Ans]

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. [Ans]
5. For a skewed distribution, the best measure of central tendency to report
a. is the mean.
b. is the median. [Ans]
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 [Ans]Note: The median is the mean of the two middle values which are 9.5 and 10.5.
e. 10.5
7. In a grouped frequency distribution the class intervals should be mutually exclusive. This means that they should be

  1. of the same length.
  2. open ended.
  3. not open-ended.
  4. not overlapping[Ans]
  5. none of the above.

8. The random variable “the number of STD phone calls made per month” is

  1. quantitative and discrete[Ans]
  2. quantitative and continuous
  3. qualitative and discrete
  4. qualitative and continuous
  5. categorical.

9. A coin is tossed five times. The probability of obtaining only one head in five tosses is

  1. 1/64
  2. 1/32[Ans]
  3. 1/16
  4. 5/16
  5. 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 Total

Yes

 96 40 136

No

 224 240 464

Total

 320 280 600

A patron is selected at random.
10. Find the probability the patron will be male.
Pr(Male) = 320/600

  1. 0.3
  2. 0.7
  3. 0.192
  4. 0.373
  5. 0.533[Ans]

11 Find the probability the patron orders dessert and is female.
Pr(Female and Yes) = 40/600

  1. 0.067[Ans]
  2. 0.106
  3. 0.693
  4. 0.627
  5. 0.160

12. Find the probability the patron is a male, given he did not order dessert.
Pr (Male given No) = 224/464

  1. 0.747
  2. 0.483[Ans]
  3. 0.373
  4. 0.300
  5. 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?

  1. 0.966
  2. 0.050
  3. 0.986
  4. 0.028
  5. 0.077

14. What is the probability there will be less than 2 inoperable machines over two days?

  1. 0.199
  2. 0.398
  3. 0.062
  4. 0.019
  5. 0.017

15. Z is the standard normal random variable. Find P(Z < 1.70)

  1. 0.3577
  2. 0.8577
  3. 0.4554
  4. 0.9554[Ans]
  5. 0.0446

16. Which of the following is not the example of compressed data

  1. data array[Ans]
  2. frequency distribution
  3. histogram
  4. ogive

17 If in a set of discrete value of observations, 50% values are greater than 25, then Q2 is:
Q2 is essentially equal to the median

  1. 20
  2. 25[Ans]
  3. 50
  4. 75

18. If quartile deviation is 8, then value of standard deviation is:
In general, QD = (2/3) SD

  1. 12[Ans]
  2. 16
  3. 24
  4. None of these

19. Which of the following is least affected by extreme values of observations in a data set
Quartile deviation is based on the first and third quartile which are about 25% above or below the extreme values.

    1. range
    2. quartile deviation[Ans]
    3. mean deviation
    4. standard deviation

20. The sum of squares of deviation from mean is:

  1. maximum[Ans]
  2. minimum
  3. zero
  4. none of these

21. The number of classes in a frequency distribution depends on:

  1. size of the data set
  2. size of the population
  3. range of the observation
  4. all of these[Ans]

22. Bayes theorem is useful in

  1. revising probability estimates
  2. computing conditional probabilities[Ans]
  3. computing sequential probabilities
  4. none of above

23. What is the probability of getting more four in rolling a dice

  1. 1/6
  2. 1/3[Ans]
  3. 1/2
  4. 1

24. If P(AB) = 0, then the events A and B are
P(AB) = 0 if A and B are mutually exclusive events

  1. independent
  2. dependent
  3. equally likely
  4. None of these[Ans]

25. If events are mutually exclusive, then

  1. Their probabilities are less than 1
  2. Their probabilities sum to one
  3. Both events can not occur at the same time[Ans]
  4. Both the events contains every out come of the event

26. Two regression lines are perpendicular to each other when

  1. r = 0
  2. r = 0.3
  3. r = -0.5
  4. r = + (-) 1[Ans]

27. Two regression coefficient are 0.8 and 0.2, then value of r is:

  1. 0.16[Ans]
  2. – 0.16
  3. 0.40
  4. – 0.40

28. The standard error of estimate is a measure of:

  1. Closeness
  2. variability
  3. Linearity [Ans]
  4. None of these

29. Forecasting time horizon includes

  1. Long range
  2. Medium range
  3. Short range
  4. All of the these[Ans]

30. Consider the time series data for the quarters of 1995 and 1996. The third quarter of 1996 would be coded as

  1. 2
  2. 3
  3. 5
  4. 6[Ans]

31. A component of time series used for short term forecasting is

  1. trend
  2. seasonal
  3. cyclical
  4. irregular [Ans]

32. The best average in the construction of then index number is

  1. median
  2. geometric mean
  3. mode
  4. arithmetic mean [Ans]

33. The Paasche index number is based on

  1. base years quantities
  2. current years quantities[Ans]
  3. average of base and current year
  4. None of the above

34. Fisher’s index number formula satisfies

  1. Circular test
  2. Factor reversal test
  3. Time reversal test
  4. Both b and c[Ans]

35. The value of correlation coefficient

  1. depends on the origin[Ans]
  2. depends on the units of scale
  3. depends on both a and b
  4. independent on a and b

36. A scatter diagram

  1. is a statistical test
  2. must be linear
  3. must be curvilinear
  4. is a graph of x and y[Ans]

37. Which of the following is the non-random method of selecting samples from the population

  1. Multistage sampling
  2. Cluster Sampling
  3. Quota Sampling[Ans]
  4. 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:

  1. 10
  2. 5
  3. 50[Ans]
  4. 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:

  1. 2.5
  2. 1.5
  3. 3.5
  4. none of the above[Ans]

40. The relationship between mean , median and mode is:

  1. Mean – median = 3(mean – mode)
  2. Mode = 3 median – 2 mean[Ans]
  3. 3 median = 2 mean + mode[Ans]
  4. All above
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