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. 19, 22, 26, 28, 30, 31, 33, 33 mean = median = mode = standard deviation =

Explanation:

Step1: Calculate the mean

Sum the data: $19 + 22 + 26 + 28 + 30 + 31 + 33 + 33 = 222$. Divide by sample size $n=8$: $\frac{222}{8} = 27.75 \approx 27.8$.

Step2: Find the median

Data is ordered: 19,22,26,28,30,31,33,33. Average 4th and 5th values: $\frac{28 + 30}{2} = 29$.

Step3: Identify the mode

Most frequent value: 33 (appears twice).

Step4: Compute standard deviation

Calculate squared differences from mean:
$(19-27.75)^2=76.5625$, $(22-27.75)^2=33.0625$, $(26-27.75)^2=3.0625$, $(28-27.75)^2=0.0625$, $(30-27.75)^2=5.0625$, $(31-27.75)^2=10.5625$, $(33-27.75)^2=27.5625$ (twice).
Sum of squared differences: $76.5625+33.0625+3.0625+0.0625+5.0625+10.5625+27.5625+27.5625=183.5$.
Sample variance: $\frac{183.5}{8-1} \approx 26.2143$. Standard deviation: $\sqrt{26.2143} \approx 5.1$.

Answer:

Mean = 27.8
Median = 29
Mode = 33
Standard Deviation = 5.1