Question

What value best represents all the measures of center for the following data set?

48, 12, 11, 45, 48, 48, 43, 32

(1 point)

Answer 1

To determine the best value that represents all the measures of center (mean, median, and mode) for the data set, we first need to calculate each of these measures.

**Data set:** 48, 12, 11, 45, 48, 48, 43, 32

1. **Mean (Average):**
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{48 + 12 + 11 + 45 + 48 + 48 + 43 + 32}{8} = \frac{239}{8} = 29.875
\]

2. **Median:**
- First, we arrange the data in ascending order: 11, 12, 32, 43, 45, 48, 48, 48
- Since there are 8 values, the median is the average of the 4th and 5th values.
\[
\text{Median} = \frac{43 + 45}{2} = \frac{88}{2} = 44
\]

3. **Mode:**
- The mode is the value that appears most frequently in the data set. Here, 48 appears three times, which is more than any other number.
\[
\text{Mode} = 48
\]

Now we summarize our findings:

- Mean: 29.875
- Median: 44
- Mode: 48

**Conclusion:**
The best value that represents all the measures of center is **48**, as it is the mode and the value representing the highest frequency in the data set.