Question

What is the five-number summary for this set of test scores?

90, 95, 89, 84, 74, 99, 97, 86, 93

(2 points)
The minimum is
. The value for Q1 is
. The median of the dataset is
. The value for Q3 is
. The maximum of the dataset is
.

Answer 1

To calculate the five-number summary (minimum, Q1, median, Q3, and maximum) for the data set of test scores, we will first sort the scores in ascending order:

**Sorted scores:** 74, 84, 89, 90, 93, 95, 97, 99

Next, we will calculate each of the five-number summary components:

1. **Minimum:** The smallest value in the dataset.
- **Minimum = 74**

2. **Maximum:** The largest value in the dataset.
- **Maximum = 99**

3. **Median:** The middle value of the dataset. Since there are 9 scores (an odd number), the median is the 5th value in the sorted list.
- **Median = 93**

4. **Q1 (First Quartile):** This is the median of the lower half of the dataset (the scores below the median). The lower half consists of: 74, 84, 89, 90 (4 values).
- Q1 is the average of the 2nd and 3rd values: (84 + 89) / 2 = 86.5
- **Q1 = 86.5**

5. **Q3 (Third Quartile):** This is the median of the upper half of the dataset (the scores above the median). The upper half consists of: 95, 97, 99 (4 values).
- Q3 is the average of the 2nd and 3rd values: (97 + 95) / 2 = 96
- **Q3 = 96**

Now we can summarize the values:

- The minimum is **74**.
- The value for Q1 is **86.5**.
- The median of the dataset is **93**.
- The value for Q3 is **96**.
- The maximum of the dataset is **99**.

So the five-number summary is:
- Minimum = 74
- Q1 = 86.5
- Median = 93
- Q3 = 96
- Maximum = 99