Central Tendency Statistical Measures

Central Tendency Statistical Measures – MCQ

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1. Which of the following is not a mathematical average?

(a) A.M.

(b) G.M.

(d) Mode.

Mode is a positional average, and not a mathematical average. So, option (d) is correct

2. The words ‘mean’ or “average” only refer to

(a) A.M.

(b) G.M.

(d) None

Just the word ‘Mean’ refers to Arithmetic Mean. So, option (a) is correct

3. Which of the following is the average of position?

(a) Median

(b) Arithmetic Mean

(d) Any of these

Median is positional Average. Arithmetic mean & Geometric mean are mathematical average. So, option (a) is correct.

4. The algebraic sum of deviations of observations from their A.M is

(a) 3

(b) 5

(d) 0

The algebraic sum of deviations of observations from their A.M. is zero. So, option (d) is correct.

5. Which relation of mode, mean and median is mostly true.

(a) Mean > Median > Mode

(b) Mean > Mode > Median

(d) 4 Mean = 3 Median – Mode

Normally, Mean > Median > Mode. So, option (a) is correct.

6. Which of the following is a measure of type of Average

(a) Median

(b) Variance

(d) (b) and (c) both.

Median is measure of Average. Variance, Standard Deviation is measure of dispersion. So, option (a) is correct.

7. Which is the following considered most suitable average for testing the level of intelligence of students

(a) Mode

(b) Arithmetic mean

(d) Median.

Median is considered most suitable average for testing the level of intelligence of students. So, option (d) is correct.

8. One of the methods to find out Mode is

(a) Mode = 3 Median + 2 Mean

(b) Mode = 2 Median – 3 Mean

(d) Mode = 3 Median -3 Mean.

Relationship among mean, median and mode is Mode = 3 Median – 2 Mean. So, option (c) is correct.

9. Mode is :

(a) Observation with highest frequency

(b) highest number of observation

(d) Any of the above

Mode is observation with highest frequency. So, option (a) is correct.

10. ‘Density Test’ is applied in

(a) Mean

(b) Median

(d) All of the above.

‘Density Test” is applied in Mode. So, option (c) is correct.

11. Which of the measures of central tendency is not affected by extreme values?

(a) Mode

(b) Median

(d) All the above.

Mode, Median & Sixth decile are not affected by extreme values. So, option (d) is correct.

12. When cumulative frequency is required to compute

(a) Mean

(b) Mode

(d) G.M.

Cumulative frequency is required to compute Median. So, option (c) is correct.

13. _____________ is a point which lie in the middle of the data set.

(a) Mean

(b) Mode

(d) S.D.

Median is a point which lie in the middle of the data set. So, option (c) is correct.

14. The suitable measure of central tendency for qualitative data is

(a) Mode

(b) Arithmetic mean

(d) Median

The suitable measure of central tendency for qualitative data is Median. So, option (d) is correct.

15. Mean of a set of values is based on

(a) All values

(b) 50 percent values

(d) Maximum &minimum value

Mean of a set of values is based on all values. So, option (a) is correct.

16. Harmonic mean gives more weightage to

(a) Small values

(b) Large values

(d) Negative values

Harmonic mean gives more weightage to small values. So, option (a) is correct.

17. Rank of median is

(a) (n + 1)/2

(b) (n + 1)/4

(d) 4(n + 1)/10

Rank of median = (n + 1)/2. So, option (a) is correct.

18. Rank of 3^rd quartile is

(a) (n + 1)/2

(b) (n + 1)/4

(d) 4(n + 1)/10

Rank of 3^rd quartile = 3(n + 1)/10. So, option (c) is correct.

19. The data 1, 2, 4, 8, 16, 32 are in

(a) Arithmetic progression

(b) Geometric progression

(d) Any of the above.

Data Values : 1 , 2 , 4 , 8 , 16 , 32, which may be expressed as : 1, (1 X 2) , (2 X 2), (4 X 2), (8 X 2), (16 X 2). Observe that common Ratio =2. So, Data is in Geometric Progression. So, option (b) is correct.

20. How many quartiles can be calculated in a series?

(a) 8

(b) 3

(d) 6.

3 quartiles can be calculated in a series. So, option (b) is correct.

21. which one is Lower quartile

(a) First quartile

(b) Second quartile

(d) Fourth quartile

First quartile is the lower quartile. So, option (a) is correct.

22. The second quartile is known as

(a) Median

(b) Lower quartile

(d) All of the above

The second quartile is known as median. So, option (a) is correct.

23. Which of the following relationship is correct?

(a) A.M. = $\displaystyle \sqrt{{}}$ (GM x HM)

(b) H.M. = $\displaystyle \sqrt{{}}$ (A.M. x G.M)

(d) G.M. = (AM + HM)

G.M. = $\displaystyle \sqrt{{}}$ (A.M. x H.M). So, option (c) is correct.

24. ______________ always lies in between the arithmetic mean & mode.

(a) G.M

(b) H.M

(d) None

Median lies between arithmetic mean & mode. So, option (c) is correct.

25. The sum of squared deviation will be minimum when taken from ________________ .

(a) Mean

(b) Median

(d) Median or mode

The sum of squared deviation will be minimum when taken from Mean. So, option (c) is correct.

26. The mean of 15 numbers is 15, if the two numbers 18 and 12 are excluded, then the mean of the remaining numbers is

(a) 15

(b) 10

(d) 24.

Sum of the 15 numbers= 15 X 15 = 225. Sum of the rest 13 numbers excluding 18 & 12 = 225 – 18 – 12 = 195. So, the average of the rest 13 numbers = 195/13=15. So, option (a) is correct.

27. If the value of mode is 25.5 and median is 16.5, the value of arithmetic mean will be

(a) 23

(b) 19

(d) 12

Mode = 25.5, Median = 16.5, Mode = 3 Median -2 Mean. Or, 2 Mean = 3 median – Mode= (3 X 16.5) – 25.5 = 49.5 – 25. 5 = 24. So, 2 x Mean = 24. Or Mean = 12. So, option (d) is correct.

28. The arithmetic mean of the observations 9, 8, 27, 36, 45 is

(a) 20

(b) 25

(d) 40

A.M = (9+8+27+36+45) /5 = 125/5=25. So, option (b) is correct.

29. If the arithmetic mean of 7, 5, 13, x and 9 be 10, then find the value x

(a) 24

(b) 36

(d) 16

A.M of the 5 values= (7 + 5 +13 + x + 9) / 5 = 10. Or, (34+x)/5 =10. Or 34+x=50. Or x=50-34=16. So, option (d) is correct.

30. If mode and median are 20 and 22 respectively, arithmetic mean shall be

(a) 27

(b) 35

(d) 28 .

Mode = 20 Median = 22. Mean = (3 Median – Mode) /2 = (3 X 22 – 20) /2 =(66 – 20)/2 = 46/2=23

So, option (c) is correct.

31. The A.M. of two numbers is 6.5 and their G.M. is 6 the two numbers are

(a) 8, 6

(b) 8, 5

(d) 4, 9.

Let two numbers be a & b. So, (a+b)/2 = 6.5, So, a+b=13. Also, Ö (ab) = 6, or ab=36. Or b=36/a.

So, a_ + (36/a)= 13. So, a² + 36 =13a, Or, a² – 13a + 36 = 0, Or, a² – 4a – 9a + 36 = 0

Or, a (a – 4 ) – 9( a – 4 ) = 0, Or, ( a – 4 ) (a – 9 ) = 0, a = 4, or, a = 9.

If a = 4, b=36/4=9. If a = 9, b=36/9=4. So, the two numbers are 4 and 9. So, option (d) is correct.

32. If the geometric mean of x, 16, 50, be 20, then the value of x is equal to

(a) 24

(b) 10

(d) 60

G.M. = ³ $\displaystyle \sqrt{{}}$ (x X 16 X 50). So, ³ $\displaystyle \sqrt{{}}$ (x X 16 X 50) = 20. So, x(16 X 50) = (20)³=20 X 20 X 20.

Or, x(16 X 50) = 20 X 20 X 20, or x=(20 X 20 X 20) / (16 X 50) = 8000/800 =10. So, option (b) is correct.

33. If arithmetic average is and geometric mean is 4, find the Harmonic Mean.

(a) 2.5

(b) 3.0

(d) 3.8.

G.M.= $\displaystyle \sqrt{{}}$ (A.M. X H.M). or, 4 = $\displaystyle \sqrt{{}}$ (5 X H.M) Or, 16 = 5 X H.M. Or, H.M. = 16/5 =3.2. So, option (c) is correct.

34. If the mean of four observations is 20 and when a constant c is added to each observation, the mean becomes 22. Find the value of c

(a) 2

(b) 3

(d) 6.

Sum of 4 Numbers = 20 x 4= 80. C is added to each observation. So, 80 + 4c =22 x 4=88.

Or, 4c = 88 – 80 = 8. Or, c = 2. So, option (a) is correct.

35. The average of 12 results is 15 and the average of the first two is14. Find the average of the rest is

(a) 15.2

(b) 15.7

(d) 14.2.

Sum of 12 numbers = 15 x 12 180. Sum of first two numbers = 14 x 2 = 28. Sum of the rest 10 numbers = 180 – 28 = 152. Average of the rest 10 numbers is 152/10=15.2. So, option (a) is correct.

36. The mean of 100 observations is 50. If one of the observations which was 50, is replaced by 40, the revised mean will be

(a) 60

(b) 49.90

(d) 40.

Sum of 100 observation = 100 x 50 = 5000. Sum of 100 observation after replacement 5,000 – 50 + 40 = 4,990. So, the revised mean = 4990/10=49.90. So, option (b) is correct.

37. The following is the data of wages per day 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8 Calculate the mode of the data

(a) 6

(b) 7

(d) 12.

The frequency of 15 data value are: 5: 4 times, 4: 1 time, 7: 3 times. 8: 4 times. 9: 2 times. 10:1 time. So, the value 8 has the highest frequency (4 times). So, mode is 8. So, option (c) is correct.

38. What is the median for the following observations?

5,8,6,9,11,4.

(a) 6

(b) 7

(d) None of these.

The 6 values in ascending order are : 4, 5, 6, 8, 9, 11. Since 6 is even number, Median is n/2 th number and the next number. So, or third and fourth number. The Third number is =6 Fourth number =8. So, the median of the 6 numbers is average of 6 and 8= (6+8)/2=7. So, option (b) is correct.

39. If the AM and HM for two numbers are 5 and 3.2 respectively then the GM will be

(a) 16.00

(b) 4.10

(d) 4.00

G.M= $\displaystyle \sqrt{{}}$ (A.M. x H.M.)= $\displaystyle \sqrt{{}}$ (5 x 3.2) = $\displaystyle \sqrt{{}}$ 16=4. So, option (d) is correct.

40. What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?

(a) 17

(b) 16

(d) 12

There is data of 8 observations. So, First Quartile = (8+1)/4 =9/4=2.25 = Second Term + (Third Term – Second Term)/4= 12+(15-12)/4= 12+3/4=12.75. So, option (c) is correct.

41. If there are two groups containing 30 and 20 observations and having 50 and 60 as arithmetic means, then the combined arithmetic mean is

a. 35

b. 56

c. 54

d. 52

N₁ = 30, x₁ = 50. N₂ = 20, x₂ = 60. So, N = N₁ + N₂= 30 + 20 = 50

Combined Arithmetic mean = x = (N₁x₁ + N₂x₂) / N = (30 x 50 + 20 x 60) /50 = (1,500 + 1,200) / 50 = 2700/50 = 54. So, option (c) is correct.

42. For continuous series, mode is given by which of the given formulae.

(a) 1+ [f₀/f₁-f₀-f₂]xi

(b) 1+ [f₁-f₀/f₁-f₀-f₂]xi

(d) 1+ [2f₁-f₀/2f₁-f₀-f₂]xi

For continuous series, mode is given by which of the given formulae shown in option (c)

43. Formula for computing median in a discrete series is

(a) Size of $\displaystyle {\left( {\frac{N}{4}} \right)}$ th item

(b) Size of $\displaystyle {\left( {\frac{{N+1}}{2}} \right)}$ th item

(d) None of the above

Formula for computing median in a discrete series given in option (b) is correct.

Central Tendency Statistical Measures – MCQ

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