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The height, h cm, of each member of a tennis club is recorded - OCR - GCSE Maths - Question 13 - 2021 - Paper 1
Question 13
The height, h cm, of each member of a tennis club is recorded. The histogram shows some of the results. 40% of the members have a height in the interval 160 < h < 1... show full transcript
Worked Solution & Example Answer:The height, h cm, of each member of a tennis club is recorded - OCR - GCSE Maths - Question 13 - 2021 - Paper 1
Step 1
Complete the histogram for the intervals 170 < h < 180
Answer
To find the frequency density for the interval 170 < h < 180, we know that 30% of the members fall within this range. Since the total number of members is not given, we can use a suitable representation. Assuming 100 members total, then:
- Members in the interval 170 < h < 180 = 30% of 100 = 30 members.
The width of this interval is (180 - 170) = 10 cm. Thus, the frequency density can be calculated as:
Therefore, the height of the bar representing this range is 3.
Step 2
Complete the histogram for the intervals 180 < h < 200
Answer
The entire range 140 < h < 200 covers 100% of the members. Since we know the intervals 160 < h < 170 and 170 < h < 180 account for 40% and 30% respectively, we can find the number of members in the interval 180 < h < 200.
So far, we have accounted for:
- 40% + 30% = 70% of the members.
Thus, the members in the interval 180 < h < 200 are:
100% - 70% = 30% of the total members.
Assuming again 100 total members, the number of members in this interval is:
- 30% of 100 = 30 members.
The width of this interval is (200 - 180) = 20 cm. Then, the frequency density for this range is:
So, the height of the bar for this range will be 1.5.