Questions: The highway fuel economy (mpg) for (a population 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, 26, 27, 29, 32, 33, 33 Mean = Median = Mode = Standard Deviation =

Solution Steps

To solve this problem, we need to calculate the mean, median, mode, and standard deviation of the given list of highway fuel economy values. Here are the high-level steps:

1. Mean: Sum all the values and divide by the number of values.
2. Median: Sort the values and find the middle value (or the average of the two middle values if the list length is even).
3. Mode: Identify the value that appears most frequently.
4. Standard Deviation: Calculate the square root of the average of the squared differences from the mean.

The mean is calculated by summing all the values and dividing by the number of values.

Given data: \( \{19, 23, 26, 27, 29, 32, 33, 33\} \)

\[ \text{Mean} = \frac{19 + 23 + 26 + 27 + 29 + 32 + 33 + 33}{8} = \frac{222}{8} = 27.75 \approx 27.8 \]

The median is the middle value when the data is sorted. If the number of values is even, the median is the average of the two middle values.

Sorted data: \( \{19, 23, 26, 27, 29, 32, 33, 33\} \)

\[ \text{Median} = \frac{27 + 29}{2} = 28 \]

The mode is the value that appears most frequently in the data set.

\[ \text{Mode} = 33 \]

The standard deviation is calculated as the square root of the average of the squared differences from the mean.

\[ \text{Standard Deviation} = \sqrt{\frac{\sum (x_i - \mu)^2}{N-1}} \]

Where \( \mu \) is the mean and \( N \) is the number of values.

\[ \text{Standard Deviation} \approx 5.0 \]

Final Answer