Q. 3.147 - Elementary Statistics

Question

A data set consists of $2m^2-1$ zeroes, one $-m$ and one $m$.

a. Compute $\hat{x}$ and $s$ for this data.

b. How many standard deviations from the mean is the observation m?

c. Assuming that $m\ge 4$, what percentage of the observations lie within three standard deviation to either side of the mean?

Step-by-Step Solution

Answer

im

Part(a) Step 1: Given information

We have been given that data set comprise of $2m^2-1$ zeroes, one $-m$ and one $m$.

We need to find out mean, that is, $\hat{x}$ and standard deviation, that is, $s.$

Part(a) Step 2: Simplify

$x_i$	$f_i$
$0$	$2m^2-1$
$-m$	$1$
$m$	$1$

Mean,