CA FOUNDATION PAPER - 3 (STATISTICS) 500+ MCQs
CHAPTER - 2 MEASURES OF CENTRAL TENDENCY
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Q.1. If X and Y are related by X-Y-10-0 and mode of X is known to be 23, then
the mode of Y is:
-
(a) 20
(b) 13
(c) 3
(d) 23
Q.2 A man travels at a speed of 20 km/hr and then returns at a speed of 30 km/hrHis average speed of the whole journey is:
-
(a) 25 km/hr
(b) 24.5 km/hr
(c) 24 km/hr
(d) None
Q.3. The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their:
-
(a) AM.
(b) HM.
(c) GM.
(d) None
Q.4 If the A.M. and H.M. for two numbers are 5 and 3.2 respectively then the G.M. will be:
-
(a) 4.05
(c) 4
(d) 4.10
(b) 16
Q.5. An aeroplane flies from A to B at the rate of 500 km/hr and comes back from B to A at the rate of 700 km/hrThe average speed of the aeroplane is:
-
(a) 600 km/hr
(b) 583.33 km/hr
(c) 100 √35 km/hr
(d) 620 km/hr.
Q.6. For a moderately skewed distribution, which of the following relationship
holds?
-
(a) Mean - Median = 3 (Median - Mode)
(b) Median -Mode = 3 (Mean -Median)
(c) Mean - Mode = 3 (Mean - Median)
(d) Mean - Median = 3 (Mean - Mode)
Q.7.________ & ___________
are called ratio averages:
-
(a) H. M. & G. M.
(c) A. M. & GM.
(b) H. M. & A. M.
(d) None
Q.8. Extreme values have effect on mode: to adu
-
(a) High
(b) low
(c) No
(d) None of these
Q.9. The mean salary for a group of 40 female workers is 5200 per month and that for a group of 60 male workers is 6800 per month. What is the combined salary?
-
(a) 6160
(b) 6280
(c) 6890
(d) 6920
Q.10 If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observations, then the combined H.Mis given by :
-
(a) 70
(b) 80
(c) 70.35
(d) 69.48
Q.11. The G.M. of 4, 6 and 8 is:
-
(a) 4.77
(b) 5.32
(c) 6.14
(d) 5.77
Q.12. G.M is a better measure than others when,
-
(a) Ratios and percentages are given
(b) Interval of scale is given
(c) Both (a) and (b)
(d) Either (a) or (b)
Q.13. The median of x, x/2, x/3, x/5 is 10. Find x where x > 0
-
(a) 24
(b) 32
(c) 8
(d) 16
Q.14. The average salary of 50 men was 80 but it was found that salary of 2 of them were 46 and 28 which was wrongly taken as 64 and 82. The revised average
salary is :
-
(a) 80
(b) 78.56
(c) 85.26
(d) 82.92
Q.15. When mean is 3.57 and mode is 2.13 then value of median is
-
(a) 3.09
(b) 5.01
(c) 4.01
(d) None of these
Q.16. The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg . and that of another five students is 125 kg., then the mean weight of the remaining students is
Q.17. In a class of 11 students, 3 students were failed in a test. 8 students who passed secured 10,11,20, 15, 12, 14, 26 and 24 marks respectively. What will be the median marks of the students:
-
(a) 12
(b) 15
(c) 13
(d) 13.5
Q.18. A lady travel at a speed of 20km/h and returned at quicker speedIf her
average speed of the whole journey is 24km/h, find the speed of return journey (in
km/h)
-
(a) 25
(b) 30
(c) 35
(d) 38
Q.19. Let the mean of the variable 'x' be 50, then the mean of u = 10 + 5x will be ?
-
(a) 250
(b) 260
(c) 265
(d) 273
Q.20. If the difference between mean and mode is 63, then the difference between
Mean and Median will______
Q.21. If the Arithmetic mean between two numbers is 64 and the Geometric mean between them is 16 The Harmonic Mean between them is
-
(a) 64
(b) 4
(c) 16
(d) 40
Q.22 The average of 5 quantities is 6 and the average of 3 is 8What is the average of the remaining two?
-
(a) 4
(b) 5
(c) 3
(d) 3.5
Q.23 The median of following numbers, which are given in ascending order is 25. Find the Value of X if data is 11, 13, 15, 19, (x+2), (x + 4) 30, 35, 39, 46
-
(a) 22
(b) 20
(c) 15
(d) 30
Q.24 The average age of a group of 10 students was 20 yearsThe average age are increased by two years when two new students joined the groupWhat is the average age of two new students who joined the group?
-
(a) 22 years
(b) 30 years
(c) 44 years
(d) 32 years
Q.25. Geometric Mean of three observations 40, 50 and X is 10The value of X is
-
(a) 2
(b) 4
(c) 1/2
(d) None of the above
Q.26. The mean of first three terms is 14 and mean of next two terms is 18 The mean
of all five terms is:
-
(a) 14.5
(b) 15
(c) 14
(d) 15.6
Q.27 The mean salary of a group of 50 persons is ₹ 5,850Later on it is discovered that the salary of one employee has been wrongly taken as 8,000 instead of 77,800The corrected mean salary is
-
(a) 5,854
(b) 5,846
(c) 5,650
(d) None of the above
Q.28. If the mode of a data is 18 and mean is 24 then median is_
-
(a) 18
(b) 24
(c) 22
(d) 21
Q.29 For data on frequency distribution of weights:
70, 73, 49, 57, 56, 44, 56, 71, 65, 62, 60, 50, 55, 49, 63 and 45
If we assume class length as 5, the number of class intervals would be
-
(a) 5
(b) 6
(c) 7
(d) 8
Q.30 The point of intersection of the "less then" and "more then" Ogives correspond to
-
(a) Mean
(c) Median
(b) Mode
(d) 10th percentile
Q.31 A man travels from Agra to Gwalior at an average speed of 30 km per hour and back at an average speed of 60 km per hour. What is his average speed?
-
(a) 38 km per hour
(b) 40 km per hour
(c) 45 km per hour
(d) 35 km per hour
Q.32. Which of the following measures of central tendency cannot be shown by graphical method?
-
(a) Mean
(b) Median
(c) Mode
(d) Quartiles
Q.33 GM of 8,4,2 is
-
(a) 4
(b) 2
(c) 8
(d) None
Q.34 The average age of 15 students is 15 yearsOut of these the average age of 5 students is 14 years and that of other 9 students is 16 years, then the age of 15th student is
-
(a) 11 years
(b) 14 years
(c) 15 years
(d) None of these
Q.35 Which of the following statement is true ?
-
(a) Median is based on all observations
(b) The Mode is the mid value
(c) The Median is the 2nd Quartile
(d) The Mode is the 5th decile
Q.36 For two numbers A.M. = 10 and G.M. = 8; the H.M....?
-
(a) 9
(b) 8.9
(c) 6.4
(d) None
Q.37 The 3rd decile for the values 15, 10, 20, 25, 18, 11, 9, 12 is
-
(a) 13
(b) 10.7
(c) 11
(d) 11.5
Q.38 A Random variables x follows uniform distribution in the interval [-3,7].Then the mean of distribution is
Q.39. If the Harmonic mean of two numbers is 4 and Arithmetic mean (A) and Geometric mean (G) satisfy the equation 2A+G^2=27 then the two numbers are
-
(a) (1,3)
(b) (9,5)
(c) (6,3)
(d) (12,7)
Q.40 There were 50 students in a class. 10 failed whose average marks were 2.5The total marks of class were 281Find the average marks of students who passed?
-
(a) 6.4
(b) 25
(c) 256
(d) 86
Q.41. If the mean of two numbers is 30 and Geometric Mean is 24 then what will be
those two numbers ?
-
(a) 36 and 24
(b) 30 and 30
(c) 48 and 12
(d) None of these
Q.42. The G.M. of observations 40, 50 and x is 10, then find the value of x?
-
(a) 4
(b) 5
(c) 2
(d) 1/2
Q.43. If the mean of data is 55.6 and the mode is 46, then the median is
-
(a) 50.4
(b) 40.7
(c) 52.4
(d) None
Q.44._______is used for ordering the size of designed cloths.
-
(a) Mean
(b) Median
(c) Mode
(d) None
Q.45. The mean of 10 observations is 14.4. Out of these mean of 4 observations is 16.5, then find the mean of remaining observations?
-
(a) 13.6
(b) 13
(c) 13.8
(d) 12
Q.46. The mean of 6, 4, 1, 5, 6, 10 and 3 is 5. If each number is added with 2, then the new mean is
-
(a) 7
(b) 5
(c) 6
(d) 10
Q.47. Which of the following is correct?
-
(a) 3(Mean - Median) = Mean - Mode
(b) Mean - Median = 3(Mean - Mode)
(c) Mean - Median = 2(Mean - Mode)
(d) Mean - Mode = 2(Mean - Median)
Q.48. A person purchases 5 rupees worth of eggs from 10 different marketsYou are to find average No. of eggs per rupee for all the markets taken together. What is the suitable form of average in this case?
-
(a) AM
(b) GM
(c) HM
(d) None
Q.49. A company's past 10 years average earnings was 40 crores. For obtaining the same average earnings for 11 years including these 10 years how much earning must be made by the company in the 11th year
Q.50. The rates of returns from three different shares are 100%, 200% and 400% respectively, the average rate of return will be and
-
(a) 350%
(b) 233.33%
(c) 200%
(d) 300%
Q.51. Mean of 7, 9, 12, x, 4, 11 & 5 is 9. Find the missing observation:
-
(a) 13
(b) 15
(c) 12
(d) None of these
Q.52. If all the frequencies are equal then which will doesn't exist :-
-
(a) Mean
(b) Median
(c) Mode
(d) None of these
Q.53.________ is the reciprocal of the AM of reciprocal of observation :
-
(a) HM
(b) GM
(c) Both
(d) none
Q.54. If each item is reduced by 15, A.M is
-
(a) reduced by 15
(b) Increased by 15
(c) reduced by 10
(d) None
Q.55. For 889, 999, 391, 384, 390, 480, 485, 760, 111, 240 Rank of median is
-
(a) 2.75
(b) 5.5
(c) 8.25
(d) None
Q.56. The average of a series of overlapping averages, each of which is based on a certain number of item within a series is known as
-
(a) Moving average
(c) Simple average
(b) Weighted average
(d) None
Q.57 If total frequencies of three series are 50,60 and 90 their means are 12, 15 and 20 respectively, then the mean of their composite series is
-
(a) 15.5
(b) 16
(c) 14.5
(d) 16.5
Q.58 If in a moderately skewed distribution the values of mode and mean are 32.1 and 35.4 respectively, then the value of the median is
-
(a) 33.3
(b) 34
(c) 34.3
(d) 33
Q.59 The median of the data 5, 6, 7, 7, 8, 9, 10, 11,11,12,15,18, 18 and 19 is
-
(a) 10
(b) 10.5
(c) 11.5
(d) 11
Q.60. The means of 20 items of a data is 5 and if each item is multiplied by 3, then the new mean will be
-
(a) 20
(b) 5
(c) 15
(d) 10
Q.61. The Geometric mean of 3, 6, 24 and 48 is
-
(a) 6
(b) 8
(c) 12
(d) 24
Q.62. Which one of the following is not a central tendency?
-
(a) Mean Deviation
(b) Arithmetic mean
(c) Median
(d) Mode
Q.63. The AM of 15 Observations is 9 and the AM of first 9 Observation is 11 and then AM of remaining Observation is
-
(a) 11
(b) 6
(c) 5
(d) 9