Question

goal: find the mean, median, and mode of a data set.
the highway mileage (mpg) for a sample of 5 different models of a car company can be found below. find the mean, median, mode and range.
21, 23, 26, 28, 28, 30
mean =
median =
mode =
range =
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Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 6$, $x_{1}=21,x_{2}=23,x_{3}=26,x_{4}=28,x_{5}=28,x_{6}=30$.
$\sum_{i=1}^{6}x_{i}=21 + 23+26+28+28+30=156$
Mean $=\frac{156}{6}=26$

Step2: Find the median

For a set of $n = 6$ (even number) data points, the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th ordered values.
The ordered data is $21,23,26,28,28,30$. $\frac{n}{2}=3$, $\frac{n}{2}+1 = 4$
Median $=\frac{26 + 28}{2}=27$

Step3: Determine the mode

The mode is the value that appears most frequently. In the data set $21,23,26,28,28,30$, the number $28$ appears twice (more frequently than other numbers)
Mode $=28$

Step4: Calculate the range

The range formula is $Range=\text{Max}-\text{Min}$. Here $\text{Max}=30$, $\text{Min}=21$
Range $=30 - 21=9$

Answer:

Mean = $26$
Median = $27$
Mode = $28$
Range = $9$