We appreciate your visit to The students in class 8B took a test Key 1 8 means 18The stem and leaf diagram shows their scores out of 40 0 6. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve these questions, let's first interpret the stem-and-leaf diagram provided:
- The key 1|8 means 18, so each 'stem' represents the tens place, and each 'leaf' represents the units place of the scores.
The scores from the stem-and-leaf diagram are:
06, 08, 08, 09, 09, 16, 25, 26, 28, 28, 29, 30, 31, 32, 33, 33, 35, 36, 37, 38, 38, 40, 40, 40, 40.
Let's count the number of students first. By adding up the leaves:
- First row: 5 students (06, 08, 08, 09, 09)
- Second row: 1 student (16)
- Third row: 6 students (25, 26, 28, 28, 29)
- Fourth row: 8 students (30, 31, 32, 33, 33, 35, 36, 37, 38, 38)
- Fifth row: 4 students (40, 40, 40, 40)
Total: 24 students
Next, let's solve each part of the question:
a. What percentage of the students had a score greater than 32?
Scores greater than 32 are: 33, 33, 35, 36, 37, 38, 38, 40, 40, 40, 40. That's 11 scores over 32.
The percentage of students with scores greater than 32 is calculated as follows:
[tex]\text{Percentage} = \left(\frac{\text{Number of students scoring > 32}}{\text{Total students}}\right) \times 100 \% = \left(\frac{11}{24}\right) \times 100 \% \approx 45.83\%[/tex]
b. What fraction of the students had a score less than 25%?
Since the test was out of 40, 25% of 40 is:
[tex]0.25 \times 40 = 10[/tex]
Scores less than 10 are: 06, 08, 08, 09, 09. That's 5 scores.
The fraction of students with scores less than 25% is:
[tex]\frac{5}{24}[/tex]
c. Any student scoring less than 40% must re-sit the test. How many students do not have to re-sit the test?
Since 40% of 40 is:
[tex]0.4 \times 40 = 16[/tex]
Students with scores 16 or above do not have to re-sit the test.
The scores are 16, 25, 26, 28, 28, 29, 30, 31, 32, 33, 33, 35, 36, 37, 38, 38, 40, 40, 40, 40 which totals to 19 students.
Therefore, 19 students do not have to re-sit the test.
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