Statistics

Find the range of the observations: $100, 150, 200, 250, 300$.

Calculate the mean deviation about the mean for the numbers $1, 2, 3$.

What is the range of the first five multiples of $11$?

Calculate the mean deviation about the mean for: $50, 60, 70$.

Determine the mean deviation about the mean for the following grouped frequency distribution:

Find the mean deviation about the mean for the repeating sequence $10, 17, 10, 17, 10, 17$.

Calculate the mean deviation about the median for the arithmetic progression: $2, 5, 8, 11, 14$.

Mean deviation about the median for the values $7, 9, 12, 13, 15, 17, 20$ is:

Which of the following is the range of the set $\{\sin(x) + \cos(x) : x \in \mathbb{R}\}$ (in the context of statistical spread, Max - Min)?

If $\sum_{i=1}^{10} |x_i - 12| = 50$, where $12$ is the mean of the 10 observations, the mean deviation about the mean is:

Calculate the variance of the set $\{0, 10\}$.

Coefficient of variation is a:

If for a sample of $10$ observations, $\sum (x_i - \bar{x})^2 = 0$, it implies:

The standard deviation of the first $7$ natural numbers is:

For a distribution, if the mean is $10$ and the sum of squares of observations is $1250$ for $n=10$, what is the standard deviation?

The variance of a set of $n$ observations is $V$. If each observation is increased by $a$, the new variance $V'$ is:

Find the variance of $4, 8, 12, 16$.

The variance of $n$ observations is $\sigma^2$. If one observation is multiplied by $k$ and all others are kept the same, what is the new mean?

Find the variance of $10, 20, 30, 40, 50$.

Two series have coefficients of variation $50$ and $60$ and their means are $15$ and $25$. Find the difference between their standard deviations.

Coefficient of Variation is expressed as a:

If the mean is $160$ and the standard deviation is $40$, find the $C.V.$

When comparing two distributions with the same arithmetic mean, the one with the smaller variance is considered to be more:

If the mean of a frequency distribution is $0$, what is the status of the $C.V.$?

If $\bar{x} = 2.5$ and $\sigma^2 = 0.25$, then $C.V.$ is:

Comparing two companies, Company A (Mean wage: $5000$, S.D.: $500$) and Company B (Mean wage: $6000$, S.D.: $540$). Which company has more uniform wages?

If all observations are identical and non-zero, the $C.V.$ is:

If the sum of squares of deviations of 10 observations from their mean 15 is 250, then the coefficient of variation is:

If the standard deviation of $x_1, x_2, \dots, x_n$ is $s$, then the standard deviation of $-x_1, -x_2, \dots, -x_n$ is:

In a distribution, if $\sum x_i = 100, \sum x_i^2 = 2500$ and $n=5$, find the standard deviation.

Find the mean deviation about the mean for $5, 10, 15, 20$.

Calculate the mean deviation about the median for $10, 10, 20, 20$.

Calculate the mean deviation about the mean for $10, 10, 20, 20$.

Find the mean deviation about the median for the data: $1, 9$.

Calculate the mean deviation about the mean for the observations: $6, 12, 18, 24, 30$.

Find the mean deviation about the median for: $10, 15, 20, 25, 30, 35$.

If each observation in a data set is multiplied by $0.5$, and the original mean deviation about the mean was $10$, what is the new mean deviation?

Calculate the mean deviation about the mean for the observations $1, 2, 4, 5$.

If the mean deviation about the mean of $1, 2, 3$ is $D$, what is the mean deviation about the mean of $10, 20, 30$?

Determine the mean deviation about the mean for the sequence $x, x+1, x+2, x+3, x+4, x+5$.

Calculate the Mean Deviation about Mean for $x = \{0, 10\}$ and $f = \{5, 5\}$.

Mean deviation about mean for grouped data $M.D.(\bar{x})$ is always:

If $\bar{x} = 25$ and $\sum f_i |x_i - 25| = 100$ with $N = 50$, find the Mean Deviation.

What is the midpoint of the class $70 - 90$?

For a distribution where all frequencies are equal and $x_i$ values are $10, 20, 30, 40, 50, 60$, find the mean deviation about the mean.

Given the distribution $x: [2, 4, 6, 8]$ and $f: [1, 3, 3, 1]$, calculate the mean deviation about the median.

Calculate the mean deviation about the mean for: $x: 100, 110, 120$ $f: 5, 10, 5$.

Compute the mean deviation about the mean for: $x$: 3, 6, 9, 12, 15 and $f$: 5, 10, 15, 10, 5.

Determine the mean deviation about the median for: Classes 0-5, 5-10, 10-15, 15-20 with frequencies 4, 6, 6, 4.

For the frequency distribution: Classes 0-20, 20-40, 40-60, 60-80 and frequencies 5, 10, 10, 5, find the mean deviation about the mean.

Mean deviation is a measure of the ________ of the data.

Which is generally the least reliable measure of dispersion for testing hypotheses?

Mean deviation does not have a property analogous to the ________ which standard deviation has.

In the calculation of mean deviation, if we change the origin of the data by adding a constant to all values, how does the mean deviation change?

The mean deviation of a dataset is $15$. If every value in the dataset is divided by $5$, the new mean deviation will be:

Which of the following is NOT a recognized limitation of mean deviation?

If the mean deviation of $10$ observations is $5$, then the sum of the absolute deviations from the mean is:

Which of the following is a specific limitation of the Mean Deviation when used in the context of 'Combined Mean' and 'Combined Dispersion' calculations for $k$ groups?

The mathematical 'robustness' of the median makes Mean Deviation about the median attractive, yet it is still limited. Why?

How does the 'Mean Deviation about the Mean' behave when the mean is not one of the observations in a discrete set?

Which measure of dispersion is the most reliable and widely used in statistics?

Calculate the standard deviation of $x: [4, 6]$ with frequencies $f: [1, 1]$.

In the calculation of standard deviation, if we use a step deviation $d_i = (x_i - A)/h$, the standard deviation $\sigma_x$ is related to $\sigma_d$ by:

If $\sum f_i = 5$, $\sum f_i x_i = 25$, and $\sum f_i x_i^2 = 145$, find the standard deviation.

A frequency distribution has $\sum f_i x_i^2 = 1000$, $\sum f_i x_i = 200$, and $N = 50$. Find the standard deviation.

Find the standard deviation for the distribution: $x: 5, 6, 7$ with $f: 2, 1, 2$.

Calculate the variance of $x: 0, 2, 4$ with frequencies $f: 1, 2, 1$.

A discrete distribution has values $x=a$ and $x=b$ with frequencies $f_a$ and $f_b$. If $f_a = f_b$, find the variance.

If the values $1, 2, \dots, n$ have frequencies $1, 1, \dots, 1$, and the standard deviation is $\sqrt{2}$, find $n$.

The standard deviation of $x_1, f_1; x_2, f_2; \dots$ is $\sigma$. What is the standard deviation of $-x_1, f_1; -x_2, f_2; \dots$?

What is the square of the standard deviation called?

If the mean of a continuous distribution is $15$ and $\frac{\sum f_i x_i^2}{N} = 250$, what is the variance?

If the variance of a distribution is $1.44$, find the standard deviation.

If $\sigma_u = 3$ and the class width $h = 4$, then $\sigma_x$ is:

Calculate the variance of the first two classes of a distribution: $0-10$ and $10-20$ with frequencies $f_1=2, f_2=3$.

If $\sum f_i u_i^2 = 100, \sum f_i u_i = 0, N = 25, h = 2$, find the standard deviation.

Find the standard deviation: Class $10-20$ (Freq 4), $20-30$ (Freq 0), $30-40$ (Freq 4).

In a continuous distribution with classes 0-20, 20-40, 40-60 and frequencies 5, 10, 5, find the standard deviation.

Calculate the variance for a continuous distribution with $N=50$, $h=4$, $\sum f_i u_i = 25$, and $\sum f_i u_i^2 = 100$.

If the sum of squares of deviations of a continuous distribution of 10 observations from their mean is 250, find the standard deviation.