Some people took part in the first round of a competition. The histogram gives information about the scores of these people in the first round. 20% of the people got a score high enough for them to qualify for the second round. Work out an estimate for the score needed to qualify for the second round. You must show all your working.

GCSE Edexcel Maths Transformations of Graphs: Some people took part in the fir

Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2

Question 18

Some people took part in the first round of a competition. The histogram gives information about the scores of these people in the first round. 20% of the people g... show full transcript

Worked Solution & Example Answer:Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2

Step 1

Find one correct frequency

96%

114 rated

Answer

To determine the frequency for each score range, we can estimate the area under each bar in the histogram since the area represents frequency.

For the range 0-10, the height is approximately 1.5, so the area is $1.5 \times 10 = 15$ .
For the range 10-20, the height is approximately 2, so the area is $2 \times 10 = 20$ .
For the range 20-30, the height is approximately 2.5, so the area is $2.5 \times 10 = 25$ .
For the range 30-40, the height is approximately 1, so the area is $1 \times 10 = 10$ .

Step 2

Find total number of people

99%

104 rated

Answer

Now, summing these areas gives us the total number of participants:

$Total = 15 + 20 + 25 + 10 = 70$

Step 3

Find 20% of the total number of people

96%

101 rated

Answer

Next, we need to find 20% of the total number of participants, which qualifies for the next round:

$20\% \text{ of } 70 = 0.2 \times 70 = 14$

Step 4

Estimate the score needed to qualify for the second round

98%

120 rated

Answer

To find the minimum score required to qualify, we need to look for the score corresponding to the top 14 people in the frequency distribution:

From the histogram:
- 0-10: 15 people
- 10-20: 20 people (Total = 35)
- 20-30: 25 people (Total = 60)
- 30-40: 10 people (Total = 70)

The top 14 scores must fall within the 20-30 range, meaning that to qualify, a score of at least 20 is required.

Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2

Worked Solution & Example Answer:Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2

Find one correct frequency

Find total number of people

Find 20% of the total number of people

Estimate the score needed to qualify for the second round

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