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There are 10 students in a class - Junior Cycle Mathematics - Question 10 - 2015
Question 10
There are 10 students in a class. All 10 of them sat a test. The table below shows the mean mark, the median mark, and the range of the marks on the test. 32 was th... show full transcript
Worked Solution & Example Answer:There are 10 students in a class - Junior Cycle Mathematics - Question 10 - 2015
Step 1
Step 2
Find what the mean, the median, and the range would be in this case.
Answer
If 2 is added to each student's mark, we can update the mean, median, and range as follows:
-
Mean Calculation:
- Original Mean: 25
- Updated Mean: 25 + 2 = 27.
-
Median Calculation:
- Original Median: 24
- Updated Median: 24 + 2 = 26.
-
Range Calculation:
- Original Range: 14
- Adding the same number (2) to all scores does not change the range, so it remains 14.
Updating the table provides:
| Results on the test | |
|---|---|
| Mean mark | 27 |
| Median mark | 26 |
| Range of the marks | 14 |
Step 3
Give an example to show that Bob is not correct.
Answer
To disprove Bob's statement, we can provide a list of numbers that has a median of 24 but does not contain the number 24:
Example List:
- 7, 23, 25, 96
To find the median:
- Arrange the numbers in ascending order: 7, 23, 25, 96
- Since there are four numbers (even number), the median is the average of the two middle values:
This example shows that even when the median is 24, it is not necessary for one of the numbers in the list to be 24.