Question

Statistics: Assignment 2.05Name:We asked 10 randomly selected students in a Speech and Debate class how manycollege courses they had passed prior to taking this class. Their responses areshown below. Find the sample mean and the median.4, 8, 14, 7, 0, 8, 2, 10, 3, 12

Answer 1

Given:

The sample is

$4,8,14,7,0,8,2,10,3,12$

Find-:

The sample mean and the median

Explanation-:

The mean formula is

$\text{ Mean }=\text{ }\frac{\text{ Sum of observations}}{\text{ Total number of observations}}$

So, mean is

$\begin{gathered} \text{ Mean }=\frac{4+8+14+7+0+8+2+10+3+12}{10} \\ \\ \text{ Mean }=\frac{68}{10} \\ \\ \text{ Mean }=6.8 \end{gathered}$

The mean is 6.8

The median is:

Total number of observation (n) = even

So, the median is

$\text{ Median }=\frac{(\frac{n}{2})^{th}\text{ term}+(\frac{n}{2}+1)^{th}\text{ term}}{2}$$\begin{gathered} n=10 \\ \\ \frac{n}{2}\text{ term }=\frac{10}{2}=5\text{ term} \\ \\ 5\text{ terms }=0 \\ \\ (\frac{n}{2}+1)\text{ terms }=6\text{ terms} \\ \\ 6\text{ term }=8 \\ \\ \end{gathered}$

The median is:

$\begin{gathered} \text{ Median }=\frac{(\frac{n}{2})^{th}\text{ term }+(\frac{n}{2}+1)^{th}\text{ term}}{2} \\ \\ \text{ Median }=\frac{0+8}{2} \\ \\ \text{ Median }=\frac{8}{2} \\ \\ \text{ Median }=4 \end{gathered}$

The median is 4