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c. for mode, if there is more than one number, separate the numbers with a \,\ e.g. 100,121.
d. the mode is
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question 10 0/1 pt 5 99 details
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 sample standard deviation. round to one decimal place as needed.
20, 23, 26, 28, 30, 32, 35, 35

a. mean = 38.88
b. median = 32
c. mode = 26,33
d. sample standard deviation = enter an integer or decimal number more...
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Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a sample $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 8$, and $\sum_{i=1}^{8}x_i=20 + 23+26+28+30+32+35+35=229$.
So, $\bar{x}=\frac{229}{8}=28.625\approx28.6$.

Step2: Calculate the median

For a set of $n = 8$ (even number of data points), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th ordered data points.
The ordered data set is $20,23,26,28,30,32,35,35$.
The $\frac{n}{2}=4$-th data point is $28$ and the $(\frac{n}{2}+1) = 5$-th data point is $30$.
Median $M=\frac{28 + 30}{2}=29$.

Step3: Calculate the mode

The mode is the data point that appears most frequently.
In the set $20,23,26,28,30,32,35,35$, the number $35$ appears twice and all other numbers appear once. So the mode is $35$.

Step4: Calculate the sample standard deviation

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$.
First, calculate $(x_i-\bar{x})^2$ for each $x_i$:

• For $x_1 = 20$: $(20 - 28.6)^2=(- 8.6)^2 = 73.96$
• For $x_2 = 23$: $(23 - 28.6)^2=(-5.6)^2 = 31.36$
• For $x_3 = 26$: $(26 - 28.6)^2=(-2.6)^2 = 6.76$
• For $x_4 = 28$: $(28 - 28.6)^2=(-0.6)^2 = 0.36$
• For $x_5 = 30$: $(30 - 28.6)^2=(1.4)^2 = 1.96$
• For $x_6 = 32$: $(32 - 28.6)^2=(3.4)^2 = 11.56$
• For $x_7 = 35$: $(35 - 28.6)^2=(6.4)^2 = 40.96$
• For $x_8 = 35$: $(35 - 28.6)^2=(6.4)^2 = 40.96$

Then $\sum_{i = 1}^{8}(x_i-\bar{x})^2=73.96+31.36 + 6.76+0.36+1.96+11.56+40.96+40.96=207.8$.

Since $n = 8$, $n-1=7$.

$s=\sqrt{\frac{207.8}{7}}\approx\sqrt{29.686}\approx5.5$.

Answer:

a. Mean = $28.6$
b. Median = $29$
c. Mode = $35$
d. Sample Standard Deviation = $5.5$