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
less or more answer both of them

Answer 1

To find the interquartile range (IQR) for Jacob's dataset, we first need to organize the data and find the quartiles.

**Jacob's times:**
14, 13, 13.5, 16, 14, 15.5, 14.5

**Step 1**: Sort the data:
13, 13.5, 14, 14, 14.5, 15.5, 16

**Step 2**: Find the median (Q2):
The median is the middle value of the sorted dataset. Since there are 7 values, the median is the 4th value:
Q2 = 14

**Step 3**: Find Q1 (the first quartile):
Q1 is the median of the first half of the data (lower half). The first half is:
13, 13.5, 14
The median of these three values is:
Q1 = 13.5

**Step 4**: Find Q3 (the third quartile):
Q3 is the median of the second half of the data (upper half). The second half is:
14, 14.5, 15.5, 16
The median of these four values is:
Q3 = (14.5 + 15.5) / 2 = 15

**Step 5**: Calculate the IQR:
IQR = Q3 - Q1 = 15 - 13.5 = 1.5 seconds

Now we can fill in the statement about Jacob's and Carl's practice times:

**Complete the statement**:
Jacob's practice times are **less** consistent than Carl's practice times because Jacob's IQR is **more** than Carl's.

In summary, Jacob's IQR is 1.5 seconds, while Carl's IQR is 1 second. This indicates that Jacob's times vary more than Carl's.