CBSE Class 11 Measures of Dispersion MCQs Set 03

Question. The calculated value of standard deviation can never be ………. .
(a) less than one
(b) more than one
(c) negative
(d) more than variance

Answer: C

Question. Which of the following mathematical sign is used to denote standard deviation?
(a) Ω
(b) σ
(c) σ2
(d) ∑

Answer: C

Question. Standard deviation is ……… of the arithmetic average of the squares of the deviations measured from the mean.
(a) square root
(b) cube root
(c) sum total
(d) None of the options

Answer: A

Question. For calculation standard deviation by step deviation method which of the following mean is used?
(a) Actual mean
(b) Assumed mean
(c) Combined mean
(d) Any of these

Answer: B

Question. Given below are the relative measures of dispersion except
(a) coefficient of variation
(b) coefficient of standard deviation
(c) standard deviation
(d) Both (a) and (b)

Answer: C

Question. Standard deviation is always computed from
(a) mean
(b)mode
(c) median
(d) geometric mean

Answer: A

Question. Standard deviation is ……… measure of dispersion.
(a) absolute
(b) relative
(c) crude
(d) Both (a) and (b)

Answer: A

Question. Coefficient of variation is given by
(a) σ / x̄
(b) x̄ / σ
(c) x̄ / σ x 100
(d) σ / x̄ x 100

Answer: D

Question. The standard deviation of a data set is expressed in the
(a) same unit as the observations in the data set
(b) square of the unit of the observation
(c) square root of the unit of the observation
(d) None of the options

Answer: A

Question. The minimum value or the lower limit of variance can be ……… .
(a) −1
(b) 0
(c) 1
(d) None of the options

Answer: B

Question. When the actual mean is multiplied with the coefficient of variation, it becomes equal to …….
(a) variance
(b) coefficient of standard deviation
(c) standard deviation
(d) coefficient of arithmetic mean

Answer: C

Question. Which of the following is a unit free number?
(a) SD
(b) Variance
(c) MD
(d) CV

Answer: D

Question. Which of the following statement is true about the most important disadvantage of standard deviation?
(a) It is used in many other statistical techniques
(b) It doesn’t takes into account all the values in the data set
(c) It is a sensitive measure of dispersion
(d) It is difficult to calculate manually

Answer: D

Question. Greater the value of standard deviation, ……… is the consistency of data.
(a) lesser
(b) greater
(c) constant
(d) None of the options

Answer: B

Question. Which of the following is not true about the measures of dispersion?
(a) It serve to locate the distribution
(b) Indicates high or low uniformity of the items
(c) Reveals how items are spread out on either side of the centre
(d) Difference or variation among the values

Answer: A

Question. Choose the incorrect statement from the options given below.
(a) Standard deviation is not based upon all the items of the series
(b) Standard deviation is the square root of variance
(c) Coefficient of standard deviation is a relative measure of dispersion
(d) All of the options

Answer: A

Question. Standard deviation remains unchanged due to change in which of the following?
(a) Change of Origin
(b) Change of Scale
(c) Change of Data
(d) All of the options

Answer: A

Assertion-Reasoning MCQs
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
(c) Assertion (A) is false, but Reason (R) is true
(d) Both are false

Question. Assertion (A): Standard deviation cannot be calculated in a mid-value frequency distribution.
Reason (R): Mid-value frequency distribution need to be converted into exclusive frequency distribution to calculate standard deviation.

Answer: D

Question. Assertion (A): When two statistical series are compared, a series with lower coefficient of variation is considered as consistent.
Reason (R): Lower value of coefficient of variation indicates lower fluctuation in the given distribution.

Answer: A

Question. Assertion (A): Any measure of central tendency can be used to compute standard deviation.
Reason (R): Standard deviation gives best result when calculated from median.

Answer: D

Question. Assertion (A): If the Variance of a series is 36, its standard deviation will be 6.
Reason (R): Variance is the square of standard deviation.

Answer: A

Case Based MCQs

You’re given the following information about the average salaries of people working in different fields.

Question. Statement I Coefficient of variation of marketing sector as per the above data is 2.5.
Statement II Coefficient of variation presents information in percentage form.
Alternatives
(a) Statement I is correct and Statement II is incorrect
(b) Statement II is correct and Statement I is incorrect
(c) Both the statements are correct
(d) Both the statements are incorrect

Answer: C

Question. Which of the following sectors pays highest salary on an average?
(a) Marketing
(b) Education
(c) Banking
(d) Technology

Answer: D

Question. Assertion (A) Marketing sector shows the least value of coefficient of variation in the given data.
Reason (R) Lower value of coefficient of variation makes it least consistent among all the given sectors.
Alternatives
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
(c) Assertion (A) is false, but Reason (R) is true
(d) Both are false

Answer: D

Question. Which of the following sectors from the above data is most consistent?
(a) Marketing
(b) Education
(c) Banking
(d) Technology

Answer: D

Question. Based upon the above data, what will be the standard deviation of the banking sector?
(a) 90,000
(b) 9,000
(c) 300
(d) 30

Answer: C

Question. The coefficient of standard deviation of the education sector will be equal to ……… .
(a) 0.03
(b) 0.3
(c) 3.33
(d) Can’t be determined

Answer: A

Question. Statement I Coefficient of variation is used to check the consistency of the data.
Statement II Standard deviation can never be calculated without arithmetic mean.
Alternatives
(a) Statement I is correct and Statement II is incorrect
(b) Statement II is correct and Statement I is incorrect
(c) Both the statements are correct
(d) Both the statements are incorrect

Answer: A

Question. Statement I Variance is the square of standard deviation for any type of statistical series.
Statement II As the sample size increases, variance becomes equal to standard deviation. Alternatives
(a) Statement I is correct and Statement II is incorrect
(b) Statement II is correct and Statement I is incorrect
(c) Both the statements are correct
(d) Both the statements are incorrect

Answer: A