Question

Longinus recorded the distance (in miles) that he biked this past week.

24, 11, 18, 8, 12, 16, 24

What is the mean, median, and mode of the data? Round your answer to the nearest tenth of a mile, if necessary.

(3 points)
The mean is
miles.

The median is
miles.

The mode is
miles.

Answer 1

To find the mean, median, and mode of the data set \( 24, 11, 18, 8, 12, 16, 24 \), follow these steps:

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

1. Sum the values:
\[
24 + 11 + 18 + 8 + 12 + 16 + 24 = 123
\]
2. Count the number of values:
There are 7 values in total.
3. Calculate the mean:
\[
\text{Mean} = \frac{123}{7} \approx 17.5714
\]
Rounding to the nearest tenth:
\[
\text{Mean} \approx 17.6
\]

### Median
The median is the middle value when the data set is ordered from least to greatest.

1. Order the values:
\[
8, 11, 12, 16, 18, 24, 24
\]
2. Find the middle value:
There are 7 values, and the middle one is the 4th value (since \( \frac{7 + 1}{2} = 4 \)):
\[
\text{Median} = 16
\]

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

1. Examine the values:
- \( 8 \) appears 1 time
- \( 11 \) appears 1 time
- \( 12 \) appears 1 time
- \( 16 \) appears 1 time
- \( 18 \) appears 1 time
- \( 24 \) appears 2 times
2. The mode is:
\[
\text{Mode} = 24
\]

### Final Answers
- The mean is **17.6** miles.
- The median is **16** miles.
- The mode is **24** miles.