Question

name:
unit 8: probability & statistics
homework 7: measures of center &
date:
per:
this is a 2 - page document!
find the mean, median, mode(s), and range of each data set. round to the nearest tenth.

1. points scored in the last 8 football games:
2. the average low temperature in colorado from october through

month | oct | nov | dec | jan | feb | mar | apr
°f | 38 | 24 | 18 | 15 | 13 | 26 | 38

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x=\{42,63,12,20,50,18,21,30\}$ and $n = 8$.
$\sum_{i=1}^{8}x_{i}=42 + 63+12+20+50+18+21+30=256$
$\bar{x}=\frac{256}{8}=32$

Step2: Find the median

First, sort the data: $12,18,20,21,30,42,50,63$.
Since $n = 8$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{4}=21$, $x_{5}=30$
$M=\frac{21 + 30}{2}=\frac{51}{2}=25.5$

Step3: Determine the mode

The mode is the number that appears most frequently. In the set $\{42,63,12,20,50,18,21,30\}$, each number appears exactly once. So, there is no mode.

Step4: Calculate the range

The range $R=\text{Max}-\text{Min}$.
$\text{Max}=63$, $\text{Min}=12$
$R=63 - 12=51$

Answer:

Mean: $32$; Median: $25.5$; Mode: None; Range: $51$