List of top Mathematics Questions on Statistics

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:

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.

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

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:

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:

If $x_1, x_2, x_3, \dots, x_n$ are $n$ observations such that $\sum (x_i + 2)^2 = 28n$ and $\sum (x_i - 2)^2 = 12n$ , then the variance is:

Let $\overline{X}$ and $\overline{Y}$ be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and $\sigma_A, \sigma_B$ are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when

Based on the following statements, choose the correct option: Statement-I: The variance of the first $n$ even natural numbers is

\frac{n^2 - 1}{4}

Statement-II: The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112.

If the variance of the frequency distribution is 160, then the value of

c \in \mathbb{N}

\begin{array}{|c|c|c|c|c|c|c|} \hline x & c & 2c & 3c & 4c & 5c & 6c \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

For the following data table

$x_i$	$f_i$
0 - 4	2
4 - 8	4
8 - 12	7
12 - 16	8
16 - 20	6

Find the value of 20M (where M is median of the data)

The frequency distribution of the age of students in a class of 40 students is given below:

$Age$	15	16	17	18	19	20
No. of Students	5	8	5	12	x	y

If the mean deviation about the median is 1.25, then

4x + 5y

Consider 10 observations

x_1, x_2, \ldots, x_{10}

\sum_{i=1}^{10} (x_i - \alpha) = 2 \quad \text{and} \quad \sum_{i=1}^{10} (x_i - \beta)^2 = 40,

\alpha, \beta

are positive integers. Let the mean and the variance of the observations be

\frac{6}{5}

\frac{84}{25}

, respectively. The value of

\frac{\beta}{\alpha}

If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:

For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.

Calculate the variance of the data set: 1, 2, 3, 5, 8, 13, 17.

The variance of the first 10 natural numbers which are multiples of 3 is:

If the mean of the data 7, 8, 9, 7, 8, 7, $\lambda$ , 8 is 8, then the variance of the data:

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

The mean deviation about the mean for the following data is:

If $M_1$ is the mean deviation from the mean of the discrete data $44, 5, 27, 20, 8, 54, 9, 14, 35$ and $M_2$ is the mean deviation from the median of the same data, then $M_1 - M_2 =$ :

The variance of the following continuous frequency distribution is:

class interval	Frequency
0 -- 4	2
4 -- 8	3
8 -- 12	2
12 -- 16	1

The standard deviation of a data set $x_1, x_2, \dots, x_6$ ( $x_i>0$ ) is 2. If

\sum_{i=1}^{9} x_i^2 = 360,

then the mean of the data set is

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