A list of 7 numbers is shown below. 17, 8, 9, 8, 14, 11, 28 (i) Find the mean of these 7 numbers, correct to 1 decimal place. (ii) Find the median of these 7 numbers. (iii) One more number is added to the list. The new median is 10.5. Find the number that was added to the list.

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A list of 7 numbers is shown below - Leaving Cert Mathematics - Question 3 - 2022

Question 3

A list of 7 numbers is shown below. 17, 8, 9, 8, 14, 11, 28 (i) Find the mean of these 7 numbers, correct to 1 decimal place. (ii) Find the median of these 7 numb... show full transcript

Worked Solution & Example Answer:A list of 7 numbers is shown below - Leaving Cert Mathematics - Question 3 - 2022

Step 1

Find the mean of these 7 numbers, correct to 1 decimal place.

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Answer

To find the mean, sum the numbers and divide by the number of values:

ext{Mean} = \frac{17 + 8 + 9 + 8 + 14 + 11 + 28}{7} = \frac{95}{7} \approx 13.6

Thus, the mean of the numbers is 13.6.

Step 2

Find the median of these 7 numbers.

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Answer

To find the median, first arrange the numbers in ascending order:

8, 8, 9, 11, 14, 17, 28

Since there are 7 numbers, the median will be the 4th number:

Median = 11.

Step 3

One more number is added to the list. The new median is 10.5. Find the number that was added to the list.

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Answer

Let the added number be x. To find the new median when one number is added, we need to average the two middle numbers when the new list is ordered. Given that the new median is 10.5, we set up the equation:

ext{Median} = \frac{(10 + 11)}{2} = 10.5

This suggests that the new number must fit into the sequence such that 10 and 11 are the two middle numbers. Therefore, the number that was added should be 10.

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