Which of the following data sets has the mini | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The variance measures the spread of data points around the mean. The formula for sample variance is $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$.For

Vedclass · Accepted Answer

$1, 2, 3, 4, 5$

Vedclass · Answer

(A) The variance measures the spread of data points around the mean. The formula for sample variance is $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$.For option $A$ $(1, 2, 3, 4, 5)$: Mean $\bar{x} = 3$. Variance $= \frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5-1} = \frac{4+1+0+1+4}{4} = \frac{10}{4} = 2.5$.For option $B$ $(1, 1, 2, 3, 6)$: Mean $\bar{x} = 2.6$. Variance $= \frac{(1-2.6)^2 + (1-2.6)^2 + (2-2.6)^2 + (3-2.6)^2 + (6-2.6)^2}{4} = \frac{2.56 + 2.56 + 0.36 + 0.16 + 11.56}{4} = \frac{17.2}{4} = 4.3$.For option $C$ $(1, 1, 2, 3, 5)$: Mean $\bar{x} = 2.4$. Variance $= \frac{(1-2.4)^2 + (1-2.4)^2 + (2-2.4)^2 + (3-2.4)^2 + (5-2.4)^2}{4} = \frac{1.96 + 1.96 + 0.16 + 0.36 + 6.76}{4} = \frac{11.2}{4} = 2.8$.For option $D$ $(1, 1, 2, 2, 5)$: Mean $\bar{x} = 2.2$. Variance $= \frac{(1-2.2)^2 + (1-2.2)^2 + (2-2.2)^2 + (2-2.2)^2 + (5-2.2)^2}{4} = \frac{1.44 + 1.44 + 0.04 + 0.04 + 7.84}{4} = \frac{10.8}{4} = 2.7$.Comparing the variances $(2.5, 4.3, 2.8, 2.7)$,the minimum variance is $2.5$ for option $A$.

Which of the following data sets has the minimum variance?

Similar Questions

If each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:

All students in a classroom performed poorly in mathematics. The teacher decided to increase the marks of each student by $10$. Which of the following statistical measures will not change even after adding the extra marks?

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

The variance and mean of $15$ observations are respectively $6$ and $10$. If each observation is increased by $8$,then the new variance and new mean of the resulting observations are respectively:

The standard deviation of the data $6, 7, 8, 9, 10$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module