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Hannah saves an amount of money each week - OCR - GCSE Maths - Question 8 - 2019 - Paper 1
Question 8
Hannah saves an amount of money each week. Here are the amounts, in pounds, that she saved in the first 5 weeks of 2019. 13 58 11 22 11 (a) Find (i) the median of... show full transcript
Worked Solution & Example Answer:Hannah saves an amount of money each week - OCR - GCSE Maths - Question 8 - 2019 - Paper 1
Step 1
Find (i) the median of the five amounts
Answer
To find the median, we first need to arrange the amounts in ascending order:
11, 11, 13, 22, 58.
The median is the middle value in this ordered list. With an odd number of amounts (5 in this case), the median is the third value:
Thus, the median is £13.
Step 2
Find (ii) the range of the five amounts
Answer
The range is calculated by subtracting the smallest amount from the largest amount. In our ordered list:
Largest amount = 58 Smallest amount = 11
Now, we compute the range:
Range = 58 - 11 = 47.
Therefore, the range of the five amounts is £47.
Step 3
Find (b) How much did she save in the 6th week?
Answer
The mean amount saved over the 6 weeks is given as £22. Total savings over 6 weeks can be calculated as:
Total savings = Mean × Number of weeks = 22 × 6 = £132.
Now, we will add the amounts saved in the first 5 weeks:
Total from the first 5 weeks = 13 + 58 + 11 + 22 + 11 = £115.
Let x be the amount saved in the 6th week:
115 + x = 132.
Solving for x gives:
x = 132 - 115 = £17.
Thus, Hannah saved £17 in the 6th week.