First, identify the median of the 12 data points, then separate the list into a lower half and an upper half based on that median. Do not include the middle values in either half.

Treat each half as its own small data set. For each half, find its median—those medians are $Q_1$ and $Q_3$.

Once you have $Q_1$ and $Q_3$, subtract $Q_1$ from $Q_3$. Then match that value to one of the answer choices.

In Desmos, type something like L = [1,2,2,3,4,4,5,5,6,6,7,9] to store all the study hours in a list named L.

On a new line, type q1 = quartile(L,1) and on another line type q3 = quartile(L,3). Desmos will display the numerical values of $Q_1$ and $Q_3$ next to q1 and q3.

On another line, type IQR = q3 - q1. The value shown for IQR is the interquartile range; compare this number with the answer choices and select the matching option.

The interquartile range (IQR) measures the spread of the middle 50% of the data and is defined as $\text{IQR} = Q_3 - Q_1$, where $Q_1$ is the first quartile and $Q_3$ is the third quartile.

The data are already listed in order:

1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 9

There are 12 data points, so the median is the average of the 6th and 7th values.

• The 6th value is 4.
• The 7th value is 5.

So the median is $(4 + 5)/2 = 4.5$.

Now split the data into a lower half and an upper half, not including the values used to find the median:

• Lower half: 1, 2, 2, 3, 4, 4
• Upper half: 5, 5, 6, 6, 7, 9

Each half has 6 numbers, so the quartiles are the averages of the middle two numbers in each half.

For the lower half (1, 2, 2, 3, 4, 4):

• The middle two values are the 3rd and 4th: 2 and 3.
• So

For the upper half (5, 5, 6, 6, 7, 9):

• The middle two values are the 3rd and 4th: 6 and 6.
• So

Use the formula $\text{IQR} = Q_3 - Q_1$:

So the interquartile range of this data set is $3.5$, which corresponds to choice C.