STATISTICS - Pyqs

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Q1
The mean of first 10 natural numbers is
(Exam: IIT-JEE Year: 1998)
(A) 4.5
(B) 5
(C) 5.5
(D) 6
Q2
If the mean of 5 observations is 8, their sum is
(Exam: NEET Year: 2016)
(A) 35
(B) 40
(C) 45
(D) 50
Q3
Variance of data \(2,2,2,2\) is
(Exam: BITSAT Year: 2014)
(A) 0
(B) 1
(C) 2
(D) 4
Q4
Standard deviation of \(3,7\) is
(Exam: JEE Main Year: 2015)
(A) 1
(B) 2
(C) \(\sqrt2\)
(D) 4
Q5
If variance is 25, SD equals
(Exam: AIIMS Year: 2010)
(A) 4
(B) 5
(C) 6
(D) 10
Q6
Mean deviation is always
(Exam: KVPY Year: 2013)
(A) negative
(B) zero
(C) positive
(D) undefined
Q7
Coefficient of variation is
(Exam: IIT-JEE Year: 2005)
(A) \(\frac{\sigma}{\bar x}\times100\)
(B) \(\sigma\bar x\)
(C) \(\frac{\bar x}{\sigma}\)
(D) \(\sigma+\bar x\)
Q8
For grouped data, assumed mean method reduces
(Exam: JEE Main Year: 2017)
(A) frequency
(B) class width
(C) calculations
(D) observations
Q9
If all observations are increased by 3, variance
(Exam: NEET Year: 2019)
(A) increases
(B) decreases
(C) unchanged
(D) becomes zero
Q10
If all observations are multiplied by 2, variance becomes
(Exam: IIT-JEE Year: 2003)
(A) doubled
(B) four times
(C) unchanged
(D) half
Q11
Mean of deviations from mean is
(Exam: Olympiad Year: 2012)
(A) 1
(B) -1
(C) 0
(D) depends
Q12
Median minimizes
(Exam: KVPY Year: 2016)
(A) squares
(B) cubes
(C) absolute deviations
(D) variance
Q13
If SD is zero, data are
(Exam: NEET Year: 2018)
(A) symmetric
(B) equal
(C) random
(D) skewed
Q14
Mean of frequencies 2,4,6,8 is
(Exam: BITSAT Year: 2015)
(A) 4
(B) 5
(C) 6
(D) 7
Q15
Combined mean of groups depends on
(Exam: IIT-JEE Year: 2001)
(A) only means
(B) only sizes
(C) both
(D) neither
Q16
Which is most affected by extreme values?
(Exam: JEE Main Year: 2020)
(A) Median
(B) Mode
(C) Mean
(D) Quartile
Q17
Step deviation uses variable \(u=\)
(Exam: AIIMS Year: 2009)
(A) \(x-a\)
(B) \(\frac{x}{h}\)
(C) \(\frac{x-a}{h}\)
(D) \(xh\)
Q18
Range equals
(Exam: NEET Year: 2017)
(A) max
(B) min
(C) max-min
(D) mean
Q19
Mean deviation about mean for symmetric data is
(Exam: Olympiad Year: 2014)
(A) max
(B) min
(C) zero
(D) undefined
Q20
Quartile deviation equals
(Exam: BITSAT Year: 2016)
(A) \(Q_3-Q_1\)
(B) \(\frac{Q_3-Q_1}{2}\)
(C) \(Q_1+Q_3\)
(D) \(Q_2\)
Q21
Shortcut formula for variance is
(Exam: IIT-JEE Year: 2004)
(A) \(\frac{\sum x^2}{n}\)
(B) \(\frac{\sum (x-\bar x)^2}{n}\)
(C) \(\frac{\sum x^2}{n}-(\bar x)^2\)
(D) \(\sum x^2-(\bar x)^2\)
Q22
Sample standard deviation uses denominator
(Exam: NEET Year: 2021)
(A) \(n\)
(B) \(n+1\)
(C) \(n-1\)
(D) \(2n\)
Q23
If 5 is added to every observation, SD becomes
(Exam: BITSAT Year: 2018)
(A) increases
(B) decreases
(C) unchanged
(D) zero
Q24
If each observation is multiplied by 3, SD becomes
(Exam: JEE Main Year: 2019)
(A) 3 times
(B) 6 times
(C) 9 times
(D) unchanged
Q25
Coding variable in step deviation method is
(Exam: AIIMS Year: 2011)
(A) \(d=x-a\)
(B) \(u=\frac{x-a}{h}\)
(C) \(u=xh\)
(D) \(u=x+a\)
Q26
Two series have same mean; better consistency is shown by smaller
(Exam: IIT-JEE Year: 2006)
(A) SD
(B) mean
(C) CV
(D) variance
Q27
Regression coefficient satisfies
(Exam: KVPY Year: 2017)
(A) \(b_{xy}b_{yx}=r\)
(B) \(b_{xy}b_{yx}=r^2\)
(C) \(b_{xy}+b_{yx}=r\)
(D) \(b_{xy}-b_{yx}=r\)
Q28
Algebraic sum of deviations from mean equals
(Exam: Olympiad Year: 2015)
(A) 1
(B) -1
(C) mean
(D) 0
Q29
Interquartile range equals
(Exam: NEET Year: 2020)
(A) \(Q_3+Q_1\)
(B) \(Q_3-Q_1\)
(C) \(\frac{Q_3-Q_1}{2}\)
(D) \(Q_2\)
Q30
Mean deviation about median is minimum when taken about
(Exam: BITSAT Year: 2019)
(A) mean
(B) mode
(C) median
(D) zero
Q31
Combined variance depends on
(Exam: IIT-JEE Year: 2007)
(A) only variances
(B) only means
(C) only sizes
(D) means, variances, sizes
Q32
Ungrouped SD formula uses
(Exam: JEE Main Year: 2016)
(A) frequencies
(B) class intervals
(C) raw observations
(D) mid-values
Q33
Grouped SD uses
(Exam: NEET Year: 2018)
(A) actual values
(B) mid-points
(C) medians
(D) modes
Q34
Short-cut SD formula uses variable
(Exam: AIIMS Year: 2012)
(A) \(x\)
(B) \(d=x-a\)
(C) \(u=x/h\)
(D) \(f\)
Q35
Standard normal distribution has mean and SD
(Exam: Olympiad Year: 2016)
(A) 0,1
(B) 1,0
(C) 0,0
(D) 1,1
Q36
Empirical relation is
(Exam: IIT-JEE Year: 2002)
(A) \(\text{Mode}=2\text{Median}-\text{Mean}\)
(B) \(\text{Mode}=3\text{Median}-2\text{Mean}\)
(C) \(\text{Mode}=2\text{Mean}-3\text{Median}\)
(D) \(\text{Mode}=\text{Mean}-\text{Median}\)
Q37
If mean = 20 and median = 18, mode equals
(Exam: NEET Year: 2015)
(A) 12
(B) 14
(C) 16
(D) 18
Q38
Variance cannot be
(Exam: BITSAT Year: 2017)
(A) zero
(B) positive
(C) negative
(D) integer
Q39
If CV of A < CV of B, then
(Exam: JEE Main Year: 2021)
(A) A more consistent
(B) B more consistent
(C) same
(D) cannot compare
Q40
Mean of deviations taken from any number equals
(Exam: IIT-JEE Year: 1999)
(A) zero
(B) minimum
(C) maximum
(D) depends
Q41
If \(b_{xy}=0\), then correlation is
(Exam: KVPY Year: 2018)
(A) 1
(B) -1
(C) 0
(D) undefined
Q42
For symmetric distribution
(Exam: Olympiad Year: 2017)
(A) Mean > Median
(B) Mean < Median
(C) Mean = Median
(D) unrelated
Q43
Mean deviation always uses
(Exam: NEET Year: 2019)
(A) signed deviations
(B) squares
(C) absolute values
(D) cubes
Q44
Quartile deviation measures spread of
(Exam: AIIMS Year: 2010)
(A) whole data
(B) middle 50%
(C) extreme values
(D) mean
Q45
SD of constants multiplied by k becomes
(Exam: IIT-JEE Year: 2008)
(A) ks
(B) k²s
(C) s/k
(D) unchanged
Q46
Median class is the class whose cumulative frequency just exceeds
(Exam: JEE Main Year: 2018)
(A) \(n\)
(B) \(n/4\)
(C) \(n/2\)
(D) \(3n/4\)
Q47
Mean of first n natural numbers is
(Exam: Olympiad Year: 2013)
(A) \(n\)
(B) \((n+1)/2\)
(C) \(n/2\)
(D) \(n+2\)
Q48
If all values equal, CV equals
(Exam: NEET Year: 2020)
(A) 100
(B) 1
(C) 0
(D) undefined
Q49
Mean minimizes sum of
(Exam: IIT-JEE Year: 2000)
(A) absolute deviations
(B) squared deviations
(C) cubes
(D) ranges
Q50
Maximum value of correlation coefficient is
(Exam: BITSAT Year: 2016)
(A) 0
(B) 1
(C) -1
(D) infinity

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