Question

the stem - and - leaf plot below shows the number of pages each student in the class read the previous evening.
0 | 0 0 5 8
1 | 2 3 5 8 8 9
2 | 2 4 6 7 7 7
3 | 3 5 6
4 | 2 4 6
5 | 7
according to the plot, 75% of students read less than
13 pages.
33 pages.
35 pages.
46 pages.

Explanation:

Step1: Count the total number of students

Count the number of leaves in the stem - and - leaf plot.
For stem \(0\): \(4\) leaves (\(0,0,5,8\))
For stem \(1\): \(6\) leaves (\(2,3,5,8,8,9\))
For stem \(2\): \(5\) leaves (\(2,4,6,7,7,7\)) (wait, no, \(2\) is the stem, and the leaves are \(2,4,6,7,7,7\) - actually \(6\) leaves)
For stem \(3\): \(3\) leaves (\(3,5,6\))
For stem \(4\): \(3\) leaves (\(2,4,6\))
For stem \(5\): \(1\) leaf (\(7\))
Total number of students \(n=4 + 6+6 + 3+3 + 1=23\)

Step2: Find the position of the 75th - percentile value

Use the formula \(i=\frac{p}{100}\times n\), where \(p = 75\) and \(n = 23\)
\(i=\frac{75}{100}\times23=17.25\)
Since \(i\) is not an integer, we round up to the next integer. So \(i = 18\)

Step3: Order the data and find the 18th value

Order the data: \(0,0,5,8,12,13,15,18,18,19,22,24,26,27,27,27,33,35,36,42,44,46,57\)
Counting the 18th value in the ordered list.
The first \(4\) values (stem \(0\)), then \(6\) values (stem \(1\)) - total \(4 + 6=10\) values so far. Then \(6\) values (stem \(2\)) - total \(10+6 = 16\) values so far. The 17th value is \(33\) (stem \(3\), leaf \(3\)), the 18th value is \(35\)

Answer:

35 pages.