Question

the highway mileage (mpg) for a sample of 8 different models of a car company can be found below. find the mean, median, mode, and standard deviation. round to one decimal place as needed.
20, 23, 25, 28, 30, 32, 35, 35
mean =
median =
mode =
standard deviation =
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Explanation:

Step1: Calculate the mean

Sum all values, divide by count.
$\text{Mean} = \frac{20 + 23 + 25 + 28 + 30 + 32 + 35 + 35}{8} = \frac{228}{8} = 28.5$

Step2: Calculate the median

Average the 4th and 5th ordered values.
$\text{Median} = \frac{28 + 30}{2} = 29.0$

Step3: Identify the mode

Find the most frequent value.
The value 35 appears twice, others once.

Step4: Calculate standard deviation

First find squared deviations from mean:
$(20-28.5)^2=72.25$, $(23-28.5)^2=30.25$, $(25-28.5)^2=12.25$, $(28-28.5)^2=0.25$,
$(30-28.5)^2=2.25$, $(32-28.5)^2=12.25$, $(35-28.5)^2=42.25$, $(35-28.5)^2=42.25$
Sum of squared deviations: $72.25+30.25+12.25+0.25+2.25+12.25+42.25+42.25=214.0$
Variance (sample, divide by $n-1$): $\frac{214.0}{7} \approx 30.571$
Standard deviation: $\sqrt{30.571} \approx 5.5$

Answer:

Mean = 28.5
Median = 29.0
Mode = 35
Standard Deviation = 5.5