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A class of 20 students took an on-line test - Junior Cycle Mathematics - Question 5 - 2014
Question 5
A class of 20 students took an on-line test. The time, in seconds, it took each student to complete the test is shown below. 15 22 17 49 12 24 15 23 8 21 16 15 20 ... show full transcript
Worked Solution & Example Answer:A class of 20 students took an on-line test - Junior Cycle Mathematics - Question 5 - 2014
Step 1
Represent the data on a stem-and-leaf diagram.
Answer
To represent the data on a stem-and-leaf diagram, we separate each number into a stem and a leaf. In this case, the stem is the first digit, and the leaf is the second digit.
Here’s how the data is organized:
Stem | Leaf
0 | 8 8
1 | 2 5 5 6 7 9
2 | 1 3 4
3 | 0 6
4 | 9
Key: 1 | 6 = 16 seconds
Step 2
Step 3
Step 4
Find the mean of the data. Give your answer correct to the nearest second.
Answer
To find the mean, we first sum all the values and then divide by the number of values.
Sum = 8 + 8 + 9 + 12 + 15 + 15 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 26 + 30 + 32 + 49 = 399
Mean = Total Sum / Number of Students = 399 / 20 = 19.95.
Rounded to the nearest second: 20 seconds.
Step 5
Step 6
Would you expect her answer to be bigger or smaller than the mean of the whole class? Give a reason for your answer.
Answer
Answer: Smaller. Reason: Seán’s time (49 seconds) is a large number, which suggests that if excluded, the calculated mean of the remaining times will be less than the mean of the whole class, which was previously calculated as 20 seconds.