Question

Jacob is practicing the 100 meter dash. the data show his times in seconds.
14,13,13.5,16,14,15.5,14.5
which box plot shows the distribution of the data
what is the interquaertile range (IQR) for Jacob's date set?

Carl is also practicing the 100 meter dash. the IQR of his practice times is 1 second. Complete the statement.

Jacob's practice times are ___ consistent than carl's practice times because jacob's IQR is ___ than carl's

Answer 1

To analyze Jacob's 100 meter dash times and determine the interquartile range (IQR), we can start with the provided data set:

**Times in seconds**: 14, 13, 13.5, 16, 14, 15.5, 14.5

### Step 1: Sort the data

Let's sort the data in ascending order:

13, 13.5, 14, 14, 14.5, 15.5, 16

### Step 2: Calculate the Quartiles

1. **Calculate the median (Q2)**:
- The median is the middle value. For 7 data points, the median is the 4th value in the sorted list, which is **14**.

2. **Calculate Q1 (1st Quartile)**:
- Q1 is the median of the lower half (first half of the data): 13, 13.5, 14
- The median of this is **13.5**.

3. **Calculate Q3 (3rd Quartile)**:
- Q3 is the median of the upper half (second half of the data): 14, 14.5, 15.5, 16
- The median of this is **14.5**.

### Step 3: Calculate the IQR

\[
\text{IQR} = Q3 - Q1 = 14.5 - 13.5 = 1
\]

### Summary of the results:
- **IQR for Jacob's data set**: 1

### Step 4: Compare with Carl's IQR

Carl's IQR is **1 second**.

### Final Statement Completion

Jacob's practice times are **equally** consistent than Carl's practice times because Jacob's IQR is **the same as** Carl's**.

### Note on Box Plot
A box plot for Jacob’s data would include:
- Minimum: 13
- Q1: 13.5
- Median (Q2): 14
- Q3: 14.5
- Maximum: 16

The box plot would depict these values, showing a cluster of values around the median.