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A six-sided numbered spinner is thrown 50 times - OCR - GCSE Maths - Question 25 - 2023 - Paper 1
Question 25
A six-sided numbered spinner is thrown 50 times. The score for each throw is recorded. Some of the results are shown in the table. An 8 was thrown f times. An unkno... show full transcript
Worked Solution & Example Answer:A six-sided numbered spinner is thrown 50 times - OCR - GCSE Maths - Question 25 - 2023 - Paper 1
Step 1
Find the total scores contributed by each score class
Answer
To find the total scores, we need to multiply each score by its frequency:
- For score 1: (1 \times 12 = 12)
- For score 3: (3 \times 2 = 6)
- For score 5: (5 \times 9 = 45)
- For score 6: (6 \times 16 = 96)
- For score 8: (8 \times f = 8f)
- For score n: (n \times 4 = 4n)
Adding these results gives us the total score: [ ext{Total Score} = 12 + 6 + 45 + 96 + 8f + 4n ]
Step 2
Set up the equation for the mean score
Answer
The mean score is given as 5.5. Therefore, we can set up the following equation based on the mean: [ \text{Mean} = \frac{\text{Total Score}}{50} = 5.5 ] This implies: [ 12 + 6 + 45 + 96 + 8f + 4n = 5.5 \times 50 ] [ 12 + 6 + 45 + 96 + 8f + 4n = 275 ]
Step 3
Solve for f and n
Answer
Combining the constants gives: [ 159 + 8f + 4n = 275 ] Subtracting 159 from both sides: [ 8f + 4n = 116 ]
Since we know there are 50 throws, we equate the frequency: [ 12 + 2 + 9 + 16 + f + 4 = 50 ] This gives: [ f + 43 = 50 ] Thus: [ f = 7 ]
Substituting (f = 7) into the score equation: [ 8(7) + 4n = 116 ] [ 56 + 4n = 116 ] Subtracting 56: [ 4n = 60 ] So: [ n = 15 ]