Question

Two friends play a card game 12 times. The winning scores are listed.


253, 266, 268, 278, 281, 286, 295, 302, 308, 315, 327, 342

Question
Determine the five-number summary of the data. Enter the answer in each box.

Response area with 5 text input boxes
Minimum:

Lower quartile:

Median:

Upper quartile:

Maximum:

Answer 1

To calculate the five-number summary (minimum, lower quartile, median, upper quartile, maximum) for the dataset, we start by reviewing the winning scores:

Scores:
253, 266, 268, 278, 281, 286, 295, 302, 308, 315, 327, 342

Now, let's determine each component step by step.

1. **Minimum**:
The minimum score is the smallest value in the dataset, which is:
- **Minimum: 253**

2. **Maximum**:
The maximum score is the largest value in the dataset, which is:
- **Maximum: 342**

3. **Median**:
To find the median, we look for the middle value. With 12 scores (even number), the median will be the average of the 6th and 7th values. The 6th value is 286 and the 7th value is 295:
\[
\text{Median} = \frac{286 + 295}{2} = \frac{581}{2} = 290.5
\]
- **Median: 290.5**

4. **Lower Quartile (Q1)**:
The lower quartile is the median of the first half of the data (the first 6 numbers).
The first half is: 253, 266, 268, 278, 281, 286. The median of this set is the average of the 3rd and 4th values (268 and 278):
\[
Q1 = \frac{268 + 278}{2} = \frac{546}{2} = 273
\]
- **Lower quartile: 273**

5. **Upper Quartile (Q3)**:
The upper quartile is the median of the second half of the data (the last 6 numbers).
The second half is: 295, 302, 308, 315, 327, 342. The median of this set is the average of the 3rd and 4th values (308 and 315):
\[
Q3 = \frac{308 + 315}{2} = \frac{623}{2} = 311.5
\]
- **Upper quartile: 311.5**

Putting it all together, the five-number summary is:

- **Minimum: 253**
- **Lower quartile: 273**
- **Median: 290.5**
- **Upper quartile: 311.5**
- **Maximum: 342**

Here are the boxes filled out:

Minimum: 253

Lower quartile: 273

Median: 290.5

Upper quartile: 311.5

Maximum: 342