Mrs. James, a sixth grade teacher, recorded how many minutes each student reported reading over winter break.

Question

Time spent reading (min.)
0
100
200
300
400
500
What was the upper quartile of the time spent reading?
minutes

Answer 1

To find the upper quartile (Q3) of the given data, we first need to organize the times spent reading in ascending order (though in this case they are already ordered):

• 0
• 100
• 200
• 300
• 400
• 500

Step 1: Determine the median (Q2). There are 6 data points. The median, or second quartile (Q2), is the average of the 3rd and 4th values.

• 3rd value: 200
• 4th value: 300

\[ Q2 = \frac{200 + 300}{2} = 250 \]

Step 2: Determine the upper quartile (Q3). The upper quartile (Q3) is the median of the upper half of the data. The upper half includes the values above the median:

• 300
• 400
• 500

There are 3 data points in the upper half. The median of this subset is the second value (the middle value):

• Median of upper half: 400

Thus, the upper quartile (Q3) is:

\[ Q3 = 400 \]

Answer: The upper quartile of the time spent reading is 400 minutes.