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Consider the following dataset - HSC - SSCE Mathematics Standard - Question 5 - 2022 - Paper 1
Question 5
Consider the following dataset. 13 16 17 17 21 24 Which row of the table shows how the median and mean are affected when a score of 5 is added to the dataset? | ... show full transcript
Worked Solution & Example Answer:Consider the following dataset - HSC - SSCE Mathematics Standard - Question 5 - 2022 - Paper 1
Step 1
How does the median change?
Answer
The median is the middle value of the dataset when it is ordered. In the original dataset, the ordered values are [13, 16, 17, 17, 21, 24]. The median for this dataset, which has an even number of values, is the average of the two middle numbers (17 and 17), resulting in a median of 17.
When we add the score of 5, the new dataset becomes [5, 13, 16, 17, 17, 21, 24]. The middle value now is 17. Since the median is affected only by the middle values of the ordered dataset, and since the addition of 5 does not alter these middle values, the median stays the same.
Step 2
How does the mean change?
Answer
The mean is calculated by summing all values and dividing by the number of values. The sum of the original dataset is:
Thus, the mean is:
After adding 5, the sum becomes:
Now, there are 7 values in total, so the new mean is:
Therefore, the mean changes with the addition of the score of 5.