Statistics Questions - JEE

For a data set having 100 observations, mean, median, mode are 50, 60, 70 respectively. If the largest 50 observations are increased by 10, then sum of new mean, median, mode equals

The mean and standard deviation of marks of 200 students were 40 and 15 respectively. Later it was discovered that a score of 40 was wrongly read as 50. The correct standard deviation is

If a variable $x$ takes values $0, 1, 2, \ldots, n$ with frequencies proportional to the binomial coefficients ${}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n$, then $\text{var}(X)$ is

Consider the frequency distribution: Class: $0$-$10$, $10$-$20$, $20$-$30$, $30$-$40$, $40$-$50$, $50$-$60$; Frequency: $3$, $a$, $b$, $11$, $8$, $4$. If the mean is $\frac{277}{9}$ and median is $\frac{335}{11}$, then the value of $4a+b$ is

Consider the following statements:(a) Mode can be computed from histogram.(b) Median is not independent of change of scale.(c) Variance is independent of change of origin and scale.

Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha,\beta$ respectively. If the variance of random variable $\alpha-\beta$ is $\dfrac{k_1}{k_2}$, where $k_1$ and $k_2$ are co-prime, then $k_1-k_2=$

The mean and standard deviation of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that one student's marks 40 was wrongly read as 50. The correct mean and standard deviation, respectively are

The mean of 5 observations $x_1, x_2, x_3, x_4, x_5$ is 5 and their variance is 124. If three of the observations are 3, 4, and 11, find $\displaystyle\sum_{i=1}^{5}|x_i - 5|$.

For a data set of 10 observations with mean $\bar{x} = 50$, $\displaystyle\sum(x_i-\bar{x})^2 = 250$. The coefficient of variation (CV) is

Mean of 100 observations is 45 and SD is 10. If 100 is mistakenly written instead of 50, the corrected standard deviation is

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt{5}$ where $k > 0$, then $k$ is equal to:

Mean of $a, b, 8, 5, 10$ is 6. Variance of the same data is 6.8. Find the values of $a$ and $b$.

Standard deviations for first 10 natural numbers is

Median of 9 distinct observations is the $\left(\dfrac{9+1}{2}\right)$th term, that is, 5th term = 20.5. If each of the largest 4 observations are increased by 2, then the median will:

In a series of $2n$ observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is 2, then $|a|$ equals

If the standard deviation of 0, 1, 2, 3, ..., 9 is $K$, then the standard deviation of 10, 11, 12, 13, ..., 19 is

If the mean deviation of numbers $1,\ 1+d,\ 1+2d,\ldots,\ 1+100d$ from their mean is 255, then $d$ is equal to

If the mean deviation of the numbers $1, 1+d, \ldots, 1+100d$ from their mean is 255, then a value of $d$ is

Mean and variance of 12 observations are 9 and $\frac{4}{2}$ (note: variance=$\frac{4}{2}$). Two values 9 and 10 were wrongly noted instead of 7 and 14. If correct variance is $\frac{m}{n}$ with $\gcd(m,n)=1$, then $m+n$ is equal to

A data consists of $n$ observations: $x_1, x_2, ..., x_n$. If $\displaystyle\sum_{i=1}^{n}(x_i + 1)^2 = 9n$ and $\displaystyle\sum_{i=1}^{n}(x_i - 1)^2 = 5n$, then the standard deviation of this data is:

In a series of $2n$ observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is 2, then $|a|$ equals

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is ______.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

What is the standard deviation of the following data?Measurement0–1010–2020–3030–40Frequency1342

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is

If $\mu$ is the mean of distribution $(y_i, f_i)$, then $\Sigma f_i(y_i - \mu) =$

If a variable takes the discrete values $\alpha - 4$, $\alpha - \dfrac{7}{2}$, $\alpha - \dfrac{5}{2}$, $\alpha - 3$, $\alpha - 2$, $\alpha + \dfrac{1}{2}$, $\alpha - \dfrac{1}{2}$, $\alpha + 5$ $(\alpha > 0)$, then the median is

The mean of a set of numbers is $\bar{X}$. If each number is divided by 3, then the new mean is

If $\displaystyle\sum_{i=1}^{9}(x_i - 5) = 9$ and $\displaystyle\sum_{i=1}^{9}(x_i - 5)^2 = 45$, then the standard deviation of the nine items $x_1, x_2, ..., x_9$ is

Consider 10 observations $x_1,x_2,\ldots,x_{10}$ such that $\displaystyle\sum_{i=1}^{10}(x_i-\alpha)=2$ and $\displaystyle\sum_{i=1}^{10}(x_i-\beta)^2=40$, where $\alpha,\beta$ are positive integers. Let the mean and the variance of the observations be $\dfrac{6}{5}$ and $\dfrac{84}{25}$ respectively. Then $\dfrac{\beta}{\alpha}$ is equal to:

If the mean and variance of five observations are $\dfrac{24}{5}$ and $\dfrac{194}{25}$ respectively and the mean of first four observations is $\dfrac{7}{2}$, then the variance of the first four observations is equal to

Let the median and the mean deviation about the median of 7 observations $170,125,230,190,210,a,b$ be $170$ and $\dfrac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is:

The mean deviation about the median of the following distribution isMarks obtained1011121415Number of students23834

The outcome of each of 30 items was observed; 10 items gave an outcome $1/2 - d$ each, 10 items gave outcome $1/2$ each and the remaining 10 items gave outcome $1/2 + d$ each. If the variance of this outcome data is $4/3$ then $|d|$ equals:

The median of a set of nine distinct observations is 20.5. If each of the last four observations of the set is increased by 2, then the median of the new set

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

Let $x_1, x_2, \ldots, x_n$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ among the following is

If in a frequently distribution, the mean and median are 21 and 22, respectively, then its mode is, approximately,

The mean weight per student in a group of seven students is 55 kg. If the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is

The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by 25, their mean remains the same. Then $\lambda$ is equal to

Let $x_1, x_2, \ldots, x_n$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be their variance.Statement-1: Variance of $2x_1, 2x_2, \ldots, 2x_n$ is $4\sigma^2$.Statement-2: Arithmetic mean of $2x_1, 2x_2, \ldots, 2x_n$ is $4\bar{x}$.

If each observation $x_i$ is increased by 5 to get new observations $x_i + 5$, then the mean deviation (MD) of the new data compared to MD of the old data is:

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt{5}$ where $k > 0$, then $k$ is equal to $2\sqrt{\dfrac{10}{3}}$. (Find the value of $a$ such that the standard deviation of four numbers $2, 4, a, 121$ along with other given constraints equals 3.5, i.e., $3a^2 - 32a + 84 = 0$.) The standard deviation of four observations is 3.5, where $\sum x_i^2 = 4 + 9 + a^2 + 121$ and $\sum x_i = 16 + a$. Find $a$.

The variance of the first n natural numbers is

For a slightly asymmetric distribution, mean and median are 5 and 6, respectively. What is its mode?

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is

A box contains 15 green balls and 10 yellow balls (total 25 balls). If 10 balls are drawn at random, find the variance of the number of green balls drawn. (Given $\sigma^2 = npq$, $n = 10$, $p = \dfrac{15}{25} = \dfrac{3}{5}$, $q = \dfrac{10}{25} = \dfrac{2}{5}$.)

Statement (a): Mode can be calculated from histogram and variance is independent of origin and scale chosen, whereas median depends on origin and scale chosen.Statement (b): Both (a) and (b) are true.Which of the following is correct regarding the above statements?

Given, $CV = 20, CV_2 = 75, \bar{x}_1 = 18$ and $\bar{x}_2 = 15$. Let $\bar{x}_1$ and $\bar{x}_2$ be the means of $1^{st}$ and $2^{nd}$ distribution respectively.

If mean and standard deviation of 5 observations $x_1, x_2, x_3, x_4, x_5$ are 10 and 3, respectively, then the variance of 6 observations $x_1, x_2, \ldots, x_5$ and $-50$ is equal to ______.

Statistics Questions (255)