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Maryam writes down the following 6 numbers, where A ∈ ℕ and A ≥ 20 : 11, 11, 12, 18, 19, A (a) Work out the median of Maryam's 6 numbers - Junior Cycle Mathematics - Question 13 - 2021
Question 13
Maryam writes down the following 6 numbers, where A ∈ ℕ and A ≥ 20 : 11, 11, 12, 18, 19, A (a) Work out the median of Maryam's 6 numbers. (b) Maryam works out the... show full transcript
Worked Solution & Example Answer:Maryam writes down the following 6 numbers, where A ∈ ℕ and A ≥ 20 : 11, 11, 12, 18, 19, A (a) Work out the median of Maryam's 6 numbers - Junior Cycle Mathematics - Question 13 - 2021
Step 1
Work out the median of Maryam's 6 numbers.
Answer
To find the median of Maryam's numbers, we first need to list them in ascending order. The numbers are:
11, 11, 12, 18, 19, A
Since A ≥ 20, the ordered set becomes:
11, 11, 12, 18, 19, A
With 6 numbers, the median is the average of the 3rd and 4th values:
Median = ( \frac{12 + 18}{2} = \frac{30}{2} = 15 )
Thus, the median is 15.
Step 2
Step 3
What will this increase do to the mean of the 6 numbers?
Answer
After increasing A by 60, the new value of A will be A + 60.
The new sum of the numbers is:
[ 71 + (A + 60) = 131 + A ]
The new mean becomes:
[ \text{New Mean} = \frac{131 + A}{6} ]
To find the increase in the mean:
[ \text{Increase in Mean} = \text{New Mean} - \text{Old Mean} ]
[ = \frac{131 + A}{6} - \frac{71 + A}{6} = \frac{131 - 71}{6} = \frac{60}{6} = 10 ]
Thus, the mean increases by 10.