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Latest TRB Tripura PGT Statistics Exam Question (Objective Questions), MCQ in English

Subjects : Statistics

Question Bank TRB Tripura PGT Statistics Exam - English
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Statistics

Question 1Single Answer
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 :
  1. A
    20
  2. B
    13
  3. C
    3
  4. D
    23
Question 2Single Answer
A man travels at a speed of 20 km/hr and then returns at a speed of 30 km/hr. His average speed of the whole journey is
  1. A
    25 km/hr
  2. B
    24.5 km/hr
  3. C
    24 km/hr
  4. D
    None
Question 3Single Answer
A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is
  1. A
    5
  2. B
    6
  3. C
    3
  4. D
    7
Question 4Single Answer
For a moderately skewed distribution, quartile deviation and the standard deviation are related by
  1. A
  2. B
  3. C
  4. D
Question 5Single Answer
The median of the data 13, 8, 11, 6, 4, 15, 2, 18 is
  1. A
    5
  2. B
    8
  3. C
    11
  4. D
    9.5
Question 6Single Answer
The sum of the squares of deviations of a set of observations has the smallest value; when the deviations are taken from their
  1. A
    A.M.
  2. B
    H. M.
  3. C
    G. M.
  4. D
    None
Question 7Single Answer
If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25 respectively, then what would be the S.D. of the combined sample size 50 ?
  1. A
    5.33
  2. B
    5.17
  3. C
    5.06
  4. D
    5
Question 8Single Answer
If two variables x & y are related by 2x + 3y –7 = 0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y about mean is
  1. A
    –5
  2. B
    4
  3. C
    12
  4. D
    50
Question 9Single Answer
Which of the following result hold for a set of distinct positive observations ?
  1. A
    A.M > G.M > H.M
  2. B
    G.M. > A.M. > H.M
  3. C
    G.M > A.M > H.M
  4. D
    A.M > G.M > H.M
Question 10Single Answer
Measures of dispersion are called averages of the ____ order .
  1. A
    1st
  2. B
    2nd
  3. C
    3rd
  4. D
    None
Question 11Single Answer
For a set of 100 observations, taking assumed mean as 4, the sum of the deviations is –11 cm and the sum of the squares of these deviations is 257 cm. The coefficient of variation is :
  1. A
    41.13%
  2. B
    42.13%
  3. C
    0.13%
  4. D
    None
Question 12Single Answer
If the AM and HM for two numbers are 5 and 3.2 respectively, then the GM will be
  1. A
    4.05
  2. B
    16
  3. C
    4
  4. D
    4.10
Question 13Single Answer
________ are used for measuring central tendency, dispersion and skewness
  1. A
    Median
  2. B
    Deciles
  3. C
    Percentiles
  4. D
    Quartiles
Question 14Single Answer
Which of the following companies A or B is more consistent so far as the payment of dividend is concerned ?
Dividend paid by A : 5 9 6 12 15 10 8 10
Dividend paid by B : 4 8 7 15 18  9  6  6
  1. A
    A
  2. B
    B
  3. C
    Both A & B
  4. D
    Neither A nor B
Question 15Single Answer
What is the coefficient of range for the following distribution ?
Class Interval : 10-19 20-29 30-39 40-49 50-59
Frequency :         11      25      16       7       3
  1. A
    22
  2. B
    50
  3. C
    75.82
  4. D
    72.46
Question 16Single Answer
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/hr. The average speed of the aeroplane is
  1. A
    600 km/hr
  2. B
    583.33 km/hr
  3. C
  4. D
    620 km/hr
Question 17Single Answer
For a moderately skewed distribution, which of the following relationship holds ?
  1. A
    Mean – Median = 3 (Median – Mode)
  2. B
    Median – Mode = 3 (Mean – Median)
  3. C
    Mean – Mode = 3 (Mean – Median)
  4. D
    Mean – Median = 3 (Mean – Mode)
Question 18Single Answer
___ & ___ are called ratio averages :
  1. A
    HM & GM
  2. B
    HM & AM
  3. C
    AM & GM
  4. D
    None
Question 19Single Answer
A sample of 35 observations has the mean 80 and S.D. as 4. A second sample of 65 observations from the same population has mean 70 and S.D. 3. The S.D. of the combined sample is :
  1. A
    5.85
  2. B
    5.58
  3. C
    10.23
  4. D
    None of these
Question 20Single Answer
If x and y are related as 3x – 4y = 20 and the quartile deviation of x is 12, then the quartile deviation of y is
  1. A
    14
  2. B
    15
  3. C
    16
  4. D
    9
Question 21Single Answer
Extreme values have ____ effect on mode .
  1. A
    High
  2. B
    low
  3. C
    No
  4. D
    None of these
Question 22Single Answer
The mean salary for a group of 40 female workers is Rs. 5,200 per month and that for a group of 60 male workers is Rs. 6,800 per month. What is the combined salary ?
  1. A
    Rs. 6,160
  2. B
    Rs. 6,280
  3. C
    Rs. 6,890
  4. D
    Rs. 6,920
Question 23Single Answer
The best measure of dispersion is
  1. A
    Q.D.
  2. B
    M.D.
  3. C
    Range
  4. D
    S.D.
Question 24Single Answer
If the mean and S.D. of x are a and b respectively, then the S.D. of  is :
  1. A
    a/b
  2. B
    –1
  3. C
    1
  4. D
    ab
Question 25Single Answer
Suppose a population A has 100 observations 101, 102, 103, ...., 200 and another population B has 100 observations 151, 152, 153, ....., 250. If VA and VB represents the variance of the two populations respectively, then VA/ VB =
  1. A
    9/4
  2. B
    1
  3. C
    4/9
  4. D
    2/3
Question 26Single Answer
If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observations then the combined H.M. is given by :
  1. A
    70
  2. B
    80
  3. C
    70.35
  4. D
    69.48
Question 27Single Answer
The G.M. of 4, 6 and 8 is
  1. A
    4.17
  2. B
    5.32
  3. C
    6.14
  4. D
    5.77
Question 28Single Answer
The Mean and S.D. for group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and S.D. as 70 and 3 respectively, what is the S.D. for the group comprising 40 observations ?
  1. A
    2.03
  2. B
    4.03
  3. C
    8.03
  4. D
    9.33
Question 29Single Answer
The Quartile deviation for the date is
x : 2 3 4 5 6
y : 3 4 8 4 1
  1. A
    1/4
  2. B
    1/2
  3. C
    1
  4. D
    0
Question 30Single Answer
If X and Y are two random variables then v(x + y) is
  1. A
    v(x) + v(y)
  2. B
    v(x) + v(y) – 2v(x, y)
  3. C
    v(x) + v(y) + 2v(x, y)
  4. D
    v(x) – v(y)
Question 31Single Answer
G.M is a better measure than others when,
  1. A
    ratios and percentages are given
  2. B
    interval of scale is given
  3. C
    Both (a) and (b)
  4. D
    Either (a) or (b)
Question 32Single Answer
Mean and S.D. of x is 50 and 5 respectively. Find mean and S.D. of  .
  1. A
    (1, 0)
  2. B
    (0, 1)
  3. C
    (1, 1)
  4. D
    (0, –1)
Question 33Single Answer
Mean and S.D. of a given set of observations is 1,500 and 400 respectively. If there is an increment of 100 in the first year and each observation is hiked by 20% in 2nd years, then find new mean and S.D.
  1. A
    1920, 480
  2. B
    1920, 580
  3. C
    1600, 480
  4. D
    1600, 400
Question 34Single Answer
If 5 is subtracted from each observation of some certain item then its coefficient of variation is 10% and if 5 is added to each item then its, coefficient of variation is 6%. Find original coefficient of variation
  1. A
    8 %
  2. B
    7.5 %
  3. C
    4 %
  4. D
    None of these
Question 35Single Answer
The median of x,  is 10. Find x where x > 0 .
  1. A
    24
  2. B
    32
  3. C
    8
  4. D
    16
Question 36Single Answer
The average salary of 50 men was Rs. 80 but it was found that salary of 2 of them were Rs. 46 and Rs. 28 which was wrongly taken as Rs. 64 and Rs. 82. The revised average salary is :
  1. A
    Rs. 80
  2. B
    Rs. 78.56
  3. C
    Rs. 85.26
  4. D
    Rs. 82.92
Question 37Single Answer
Inter Quartile Range is _____ of Quartile Deviation .
  1. A
    Half
  2. B
    Double
  3. C
    Triple
  4. D
    Equal
Question 38Single Answer
The sum of squares of deviation from mean of 10 observations is 250. Mean of the data is 10. Find the coefficient of variation .
  1. A
    10 %
  2. B
    25 %
  3. C
    50 %
  4. D
    0 %
Question 39Single Answer
If A be the A.M. of two positive unequal quantities X and Y and G be their G.M., then ;
  1. A
    A < G
  2. B
    A > G
  3. C
    A < G
  4. D
    A > G
Question 40Single Answer
When mean is 3.57 and mode is 2.13 then the value of median is
  1. A
    3.09
  2. B
    5.01
  3. C
    4.01
  4. D
    None of these
Question 41Single Answer
If L1 = highest observation and L2 = smallest observation, then Coefficient of Range =
  1. A
  2. B
  3. C
  4. D
Question 42Single Answer
The equation of a line is 5x + 2y = 17, Mean deviation of y about mean is 5. Calculate mean deviation of x about mean .
  1. A
    –2
  2. B
    2
  3. C
    –4
  4. D
    None
Question 43Single Answer
If variance of x is 5, then find the variance of (2 – 3x)
  1. A
    10
  2. B
    15
  3. C
    5
  4. D
    – 13
Question 44Single Answer
The harmonic mean of 1, 1/2, 1/3 ... 1/n is
  1. A
    1 / (n + 1)
  2. B
    2 / (n + 1)
  3. C
    (n + 1) / 2
  4. D
    1 / (n – 1)
Question 45Single Answer
The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg. and of another five students is 125 kg. then the mean weight of the remaining students is
  1. A
    120
  2. B
    105
  3. C
    115
  4. D
    None of these
Question 46Single Answer
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
  1. A
    12
  2. B
    15
  3. C
    13
  4. D
    13.5
Question 47Single Answer
The variance of data : 3, 4, 5, 8 is
  1. A
    4.5
  2. B
    3.5
  3. C
    5.5
  4. D
    6.5
Question 48Single Answer
A lady travel at a speed of 20 km/h and returned at quicker speed. If her average speed of the whole journey is 24 km/h, find the speed of return journey (in km/h)
  1. A
    25
  2. B
    30
  3. C
    35
  4. D
    38
Question 49Single Answer
Let the mean of the variable 'x' be 50, then the mean of u = 10 + 5x will be
  1. A
    250
  2. B
    260
  3. C
    265
  4. D
    273
Question 50Single Answer
Given the observations 4, 9, 11, 14, 37. The Mean deviation about the Median is
  1. A
    11
  2. B
    8.5
  3. C
    7.6
  4. D
    7.45
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