Question

homework 6.1 - describing data
score: 44.51/100 answered: 13/21
question 16
goal: find the mean, median, and mode of a data set.
consider the data set
2 4 3 2 1 9
find the average (mean):
find the median:
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Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x_1 = 2,x_2=4,x_3 = 3,x_4=2,x_5 = 1,x_6=9$, and $n = 6$.
$\sum_{i=1}^{6}x_{i}=2 + 4+3 + 2+1+9=21$.
$\bar{x}=\frac{21}{6}=3.5$.

Step2: Calculate the median

First, order the data set: $1,2,2,3,4,9$.
Since $n = 6$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{\frac{6}{2}}=x_3 = 2$, $x_{\frac{6}{2}+1}=x_4 = 3$.
$M=\frac{2 + 3}{2}=2.5$.

Step3: Calculate the mode

The mode is the number that appears most frequently in the data set.
In the data set $1,2,2,3,4,9$, the number $2$ appears twice, and other numbers appear only once. So the mode is $2$.

Answer:

The mean is $3.5$, the median is $2.5$, and the mode is $2$.