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. $$ 19,23,25,27,30,31,33,33 $$ Mean $$ =27.8 $$ Median $$ =28.5 $$ Mode $$ =33 $$ Standard Deviation $$ = $$

Question

UpStudy AI · Accepted Answer

To calculate the **standard deviation** for the given dataset:

$$
19, \, 23, \, 25, \, 27, \, 30, \, 31, \, 33, \, 33
$$

with a **mean (average)** of $$27.8$$, follow these steps:

### 1. Calculate Each Deviation from the Mean and Square It

$$
\begin{align*}
(19 - 27.8)^2 &= (-8.8)^2 = 77.44 \
(23 - 27.8)^2 &= (-4.8)^2 = 23.04 \
(25 - 27.8)^2 &= (-2.8)^2 = 7.84 \
(27 - 27.8)^2 &= (-0.8)^2 = 0.64 \
(30 - 27.8)^2 &= 2.2^2 = 4.84 \
(31 - 27.8)^2 &= 3.2^2 = 10.24 \
(33 - 27.8)^2 &= 5.2^2 = 27.04 \
(33 - 27.8)^2 &= 5.2^2 = 27.04 \
\end{align*}
$$

### 2. Sum All Squared Deviations

$$
77.44 + 23.04 + 7.84 + 0.64 + 4.84 + 10.24 + 27.04 + 27.04 = 178.12
$$

### 3. Calculate the Variance

Since this is a **sample** of 8 models, use $$ n - 1 = 7 $$ for the variance:

$$
\text{Variance} = \frac{178.12}{7} \approx 25.45
$$

### 4. Compute the Standard Deviation

$$
\text{Standard Deviation} = \sqrt{25.45} \approx 5.0 \, \text{(rounded to one decimal place)}
$$

### **Final Answer**

$$
\text{Standard Deviation} = 5.0
$$
The standard deviation is 5.0.

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. \( 19,23,25,27,30,31,33,33 \) Mean \( =27.8 \) Median \( =28.5 \) Mode \( =33 \) Standard Deviation \( = \)

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