Question

Calculate the values for the 5-number summary of the skewed dataset 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25.(2 points)
The minimum value=
. Quartile 1=
. The median=
. Quartile 3=
. The maximum value=
.

Answer 1

To calculate the 5-number summary (minimum, Quartile 1 (Q1), median, Quartile 3 (Q3), and maximum) for the dataset \( 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25 \), we can follow these steps:

1. **Minimum Value**: The smallest value in the dataset.

- **Minimum = 11**

2. **Maximum Value**: The largest value in the dataset.

- **Maximum = 25**

3. **Median**: The median is the middle value when the data is sorted. Since there are 11 data points (an odd number), the median will be the 6th value.

- The sorted dataset is already in order: \( 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25 \)
- **Median = 13** (the 6th value)

4. **Quartile 1 (Q1)**: Q1 is the median of the first half of the dataset (the lower half). This includes the first 5 data points.

- First half: \( 11, 12, 12, 13, 13 \)
- Median of the first half (5 data points): the 3rd value, which is 12.
- **Q1 = 12**

5. **Quartile 3 (Q3)**: Q3 is the median of the second half of the dataset (the upper half). This includes the last 5 data points.

- Second half: \( 13, 14, 14, 15, 19, 25 \)
- Median of the second half (5 data points): the 8th value from the sorted dataset which is 14.
- **Q3 = 19**

Now, compiling all values:

- Minimum = 11
- Q1 = 12
- Median = 13
- Q3 = 19
- Maximum = 25

### Final 5-number summary:

- Minimum: **11**
- Q1: **12**
- Median: **13**
- Q3: **19**
- Maximum: **25**