List of top Mathematics Questions on Statistics asked in CUET (UG)

Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:

Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:

Let F(Z) be the cumulative density function of the standard normal variate Z, then which of the following are correct?
(A) \(F(Z) = \int_{-\infty}^{Z} \frac{1}{\sqrt{2\pi}} e^{-z^2/2} dz, -\infty < Z <\infty\)
(B) \(F(-Z) = 1 - F(Z)\)
(C) \(F(0) = 0\)
(D) \(F(\infty) = 1\)
Choose the correct answer from the options given below:

If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation s = 50, then the size of the sample in the study is:
(Given \(Z_{0.025}\) = 1.96)

If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation s = 50, then the size of the sample in the study is:
(Given \(Z_{0.025}\) = 1.96)

Let F(Z) be the cumulative density function of the standard normal variate Z, then which of the following are correct?
(A) \(F(Z) = \int_{-\infty}^{Z} \frac{1}{\sqrt{2\pi}} e^{-z^2/2} dz, -\infty < Z <\infty\)
(B) \(F(-Z) = 1 - F(Z)\)
(C) \(F(0) = 0\)
(D) \(F(\infty) = 1\)
Choose the correct answer from the options given below:

If a\(95\% \)confidence interval for the population mean was reported to be 160 to 170 and\(σ = 25\), then the size of the sample used in this study is:

Which of the following are components of a time series?(A) Irregular component
(B) Cyclical component
(C) Chronological component
(D) Trend Component
Choose the correct answer from the options given below:

Mohan caught 100 frogs from a garden and measured their weights. The mean weight of these frogs is a :

A sample size of \(x\) is considered to be sufficient to hold the Central Limit Theorem (CLT). The value of \(x\) should be:

The following data is from a simple random sample: 15, 23, x, 37, 19, 32. If the point estimate of the population mean is 23, then the value of x is:

For the given five values 12, 15, 18, 24, 36; the three-year moving averages are:

Match List-I with List-II:

List-I	List-II
(A) Distribution of a sample leads to becoming a normal distribution	(I) Central Limit Theorem
(B) Some subset of the entire population	(II) Hypothesis
(C) Population mean	(III) Sample
(D) Some assumptions about the population	(IV) Parameter

Choose the correct answer from the options given below.

Consider the following statements :
A. Cost of living at two different cities can be compared with volume index.
B. When the prices of rice are to be compared we use price index.
C. In Laspeyre's price index number weight is considered as price in current year.
D. Purchasing power of money can be assessed through consumer price index.
E. Fisher Index number is called ideal index number.
Choose the correct answer from the options given below :

Match List - I with List - II.

List - I	List -II
(A) t-distribution	(I)sample size\(\geq30\)
(B) Sample mean	(II)\(X\)
(C) Population mean	(III)degree of freedom
(D)Z-distribution	(IV)\(\mu\)

Choose the correct answer from the options given below:

The index number of base yera is :

Match List I with List II:

List I		List II
A.	Marshall Edgeworth's Index Number	I.	\(\frac{\sum p_1q_0}{\sum p_0q_0}\times100\)
B.	Laspeyre's Index Number	II.	\(\sqrt{\frac{\sum p_1q_0}{\sum p_0q_0}\times\frac{\sum p_1q_1}{\sum p_0q_1}}\times100\)
C.	Fisher's Ideal Index Number	III.	\(\frac{\sum p_1q_1}{\sum p_0q_1}\times100\)
D.	Paasche's Index Number	IV.	\(\frac{\sum p_1(q_0+q_1)}{\sum p_0(q_0+q_1)}\times100\)

Consider the table below on the quantities of commodities alongside their prices in the year 2020 and 2022.

Commodity	Prices (₹)		Quantities
	In 2020 Year	In 2022 Year	In 2020 Year	In 2022 Year
A	1	2	5	6
B	3	4	3	4
C	5	6	2	5
D	4	5	1	3
E	3	4	4	6

The value of ∑p₁q₀ is :

Match List I with List II

LIST I		LIST II
A.	Weight is considered as quantity in base year in,	I.	Paasche's index number
B.	Weight is considered as quantity in current year in,	II.	Fisher's index number
C.	The index number which is called as ideal index number is,	III.	Marshall-Edgeworth's index number
D.	Weight is taken as the average of the base year quantity and current year quantity in	IV.	Laspeyre's index number

Choose the correct answer from the options given below:

Consider the following data:

Year	2008	2009	2010	2011	2012
Production(In Tons)	60	75	80	70	85

The equation of the straight line trend by the method of least squares is,

For a certain data test statistic ‘t’ is calculated as : \(|t|=|\frac{65-68}{\frac{4}{\sqrt{15}}}|=2.90\), then select the correct option :

The price relatives and weights of a set of commodities are given as:

Commodity	P	Q	R
Price Relative	100	130	180
Weight	x	2x	y

If the sum of weights is 54 and index for the set is 130, then the values of x and y are

If Paasche's index number is 160 and Laspeyre's index number is 250, then Fisher's index number is: