Question

pre - algebra
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assignment
name______________________________ id
date_______________ period
find the median and mean for each data set. is there an outlier? if so, what is it?

1. hits in a round of hacky sack

8 10 8 6 2 9 3 12
13 13
mean 8.4
median 8.5
outlier? 2

Explanation:

Step1: Sort the data set

Sorted data: $2, 3, 6, 8, 8, 9, 10, 12, 13, 13$

Step2: Calculate the mean

Sum of values: $2+3+6+8+8+9+10+12+13+13=84$
Mean: $\frac{84}{10}=8.4$

Step3: Calculate the median

Average 5th & 6th values: $\frac{8+9}{2}=8.5$

Step4: Identify outliers

Calculate IQR:
Q1 (25th percentile): $\frac{3+6}{2}=4.5$
Q3 (75th percentile): $\frac{12+13}{2}=12.5$
IQR = $12.5-4.5=8$
Lower fence: $4.5 - 1.5\times8=4.5-12=-7.5$
Upper fence: $12.5 + 1.5\times8=12.5+12=24.5$
Only $2$ is not an outlier (it lies within $-7.5$ to $24.5$); there are no outliers.

Answer:

Mean: $8.4$
Median: $8.5$
Outlier: None (the value 2 is not an outlier as it falls within the calculated fence range)