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UPSC CDS  Statistics- Question papers Selection Exam 2012   Objective Questions  Statistics Part - I

1.  Class size is the difference between the class marks of two

(b) classes

(c) alternate classes

(d) None of these

Hints & Solutions  :  Class size is the difference between the class marks of two adjacent classes.

2.  In bar chart, the gap between the bars is always

(a) same  (Ans)

(b) zero

(c) varies

(d) can't say

Hints & Solutions  :  Clearly, same.

3.  Histogram is

(a) one dimensional

(b) two dimensional   (Ans)

(c) three dimensional

(d) None of these

Hints & Solutions  :  Clearly, histogram is a two dimensional figure.

4.  Joining the mid-points of the respective tops in histogram, we get

(a) Bar chart

(b) Pie chart

(c) Ogive

(d) Frequency polygon   (Ans)

Hints & Solutions  :  Frequency polygon.

5.  The most stable measure of central tendency is

(a) the median

(b) the mean  (Ans)

(c) the mode

(d) None of these

6.  The measure which takes into account all the data items is

(a) mean   (Ans)

(b) frequency

(c) mode

(d) median

Hints & Solutions  :  Mean

7.  Consider the following statement

(i) A bar graph is two dimensional

(ii) In a histogram, the height as well as the width of each rectangle matters

(iii) In a bar graph, not only height, but also  width of each rectangle matters.

(iv) In a bar graph, height of each rectangle matters and not its width of these statements

(a) (i) alone is true

(b) All the true

(c) (iii) and (iv) are true   (Ans)

(d) (ii) and (iv) are true

8.  In a bar chart, what does matter is

(a) length of y-axis

(b) length of x-axis

(c) width of the bar   (Ans)

(d) length of the bar

Hints & Solutions  :  Width of the rectangle only makes it pictorially more attractive.

9.  Frequency polygon can be drawn after drawing

(a) Ogive

(b) Bar chart

(c) Histogram   (Ans)

(d) None of these

Hints & Solutions  :  Frequency polygon can be drawn by joining the mid-points of the respective tops in histogram.

10.  Pie-chart is drawn with the help of

(b) chords of the circle

(c) sectors of the circle   (Ans)

(d) diameter of the circle

Hints & Solutions  :  Pie-chart is drawn with the help of sectors of the circle the angle of sector depends upon the percentage of the quantity showing.

11.  The total expenditure incurred by an industry under different heads is best presented as a

(a) Pie diagram    (Ans)

(b) Histogram

(c) Frequency polygon

(d) Bar chart

12.  Which one of the following is a source of data for primary investigations ?

(a) News Papers

(b) Magazines

(c) Questionnaires    (Ans)

(d) All of these

Hints & Solutions  :  Primary investigation is done by questionnaires.

13.  Pie diagrams used to represent statistical data are

(a) one dimensional    (Ans)

(b) two dimensional

(c) three dimensional

(d) None of these

14.  An ogive is used to determine

(a) Mean

(b) Median    (Ans)

(c) GM

(d) HM

Hints & Solutions  :  An ogive is used to determine the median.

15.  The graph of frequency distribution is

(i)    Histogram

(ii)   Frequency curve

(iii)  Ogive

(iv)  Frequency polygon

(a) (i), (ii) and (iv)   (Ans)

(b) (ii) and (iii) only

(c) (i), (ii) and (iii)

(d) All are correct

16. A distribution which exhibits real gaps is called

(a) Frequency distribution

(b) Cumulative frequency distribution

(c) Discrete distribution    (Ans)

(d) Continuous distribution

Hints & Solutions  :  Discrete distribution exhibits real gaps. Also in this type of distribution exact measurements of the units are clearly shown.

17.  The mid value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are

(a) 37.5 and 47.5

(b) 47 and 37

(c) 37 and 47   (Ans)

(d) 47.5 and 37.5

Hints & Solutions  :  Let the lower limit be x. Then, the upper limit of class interval = x + 10

∴    x + (x + 10)  = 42
2

⇒         2x + 10 = 84

⇒               2x  = 74

⇒                 x  = 37

∴    Lower limit = 37, Upper Limit = 37 + 10 = 47

18.  The actual lower class limits of the following classes 10-19, 20-29, 30-39 and 40-49 are

(a) 9.5, 19, 29 and 39.5

(b) 10, 20, 30 and 40

(c) 9.5, 19.5, 29.5 and 39.5   (Ans)

(d) 18.5, 28.5, 38.5 and 48.5

Hints & Solutions  :  True lower class limit are obtained by subtracting 0.5 from the lower limit so, clearly 9.5, 19.5, 29.5 and 39.5.

19.  State which of the following variable are discrete

i. Number of children in a family

ii. Wages of workers

iii. The ages of students

iv. Weights of a set of a students

(a) All of these

(b) (i), (ii) and (iii) only    (Ans)

(c) (i) and (ii) only

(d) None of these

Hints & Solutions  :  A discrete frequency distribution is such a distribution in which data are presented in a way that exact measurements of the units are clearly shown. So clearly weights of a set of a students is continuous. while other three as discrete.

20.  If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11, then the mean of first three observations is :

(a) 9   (Ans)

(b) 11

(c) 13

(d) None of these

Hints & Solutions  :  Here sum of 5 observations

= x + (x + 2) + (x + 4) + (x + 6) + (x + 8)

= 5x + 20

∴    Mean of total observations =  5x + 20  = 11
5

⇒                        5x + 20 = 55

⇒                                        x = 7

∴                Mean of first three =  x + (x + 2) + (x + 4)
3

= 3x + 6   = 27 = 9
6          3