Question

Find the measures of center—mean, median, and mode—for the given dataset. If needed, express your answer as a decimal rounded to the nearest tenth.

10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17

(2 points)
mean:
; median:
; mode:

Answer 1

To calculate the measures of center for the dataset \( 10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17 \), we will find the mean, median, and mode.

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

1. **Sum the numbers**:
\[
10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17 = 10 + 17 = 27
\]
\[
27 + 11 = 38 \\
38 + 24 = 62 \\
62 + 12 = 74 \\
74 + 7 = 81 \\
81 + 15 = 96 \\
96 + 17 = 113 \\
113 + 20 = 133 \\
133 + 5 = 138 \\
138 + 11 = 149 \\
149 + 21 = 170 \\
170 + 16 = 186 \\
186 + 17 = 203
\]
The total sum is **203**.

2. **Count the numbers**:
There are **14** numbers in the dataset.

3. **Calculate the mean**:
\[
\text{Mean} = \frac{\text{sum of values}}{\text{number of values}} = \frac{203}{14} \approx 14.5
\]

### Median
The median is the middle value when the numbers are sorted. If there is an even number of observations, it is the average of the two middle values.

1. **Sort the numbers**:
\[
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
\]

2. **Find the middle position**:
Since there are 14 numbers (even), the median will be the average of the 7th and 8th values.

The 7th value is **15** and the 8th value is **16**.

3. **Calculate the median**:
\[
\text{Median} = \frac{15 + 16}{2} = \frac{31}{2} = 15.5
\]

### Mode
The mode is the number that appears most frequently in the dataset.

1. **Count the frequency of each number**:
- 5: 1
- 7: 1
- 10: 1
- 11: 2
- 12: 1
- 15: 1
- 16: 1
- 17: 3
- 20: 1
- 21: 1
- 24: 1

The number **17** appears **3 times**, which is more than any other number.

### Summary
- **Mean**: 14.5
- **Median**: 15.5
- **Mode**: 17

**Final Answer**:
- mean: 14.5
- median: 15.5
- mode: 17