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The ages of the people who attended a music concert was summarised in the table below - NSC Mathematics - Question 2 - 2023 - Paper 2
Question 2
The ages of the people who attended a music concert was summarised in the table below. | AGE | NUMBER OF PEOPLE | | 5 < x ≤ 15 | 20 | | ... show full transcript
Worked Solution & Example Answer:The ages of the people who attended a music concert was summarised in the table below - NSC Mathematics - Question 2 - 2023 - Paper 2
Step 1
Step 2
Step 3
On the grid provided in the ANSWER BOOK, draw a cumulative frequency graph (ogive) to represent the above data.
Answer
To create the cumulative frequency graph:
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Calculate the cumulative frequency for each age group:
- For 5 < x ≤ 15: 20
- For 15 < x ≤ 25: 20 + 25 = 45
- For 25 < x ≤ 35: 45 + 60 = 105
- For 35 < x ≤ 45: 105 + 55 = 160
- For 45 < x ≤ 55: 160 + 40 = 200
- For 55 < x ≤ 65: 200 + 30 = 230
- For 65 < x ≤ 75: 230 + 30 = 260
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Plot these points on the grid using the upper limits of the intervals:
- Plot (15, 20)
- Plot (25, 45)
- Plot (35, 105)
- Plot (45, 160)
- Plot (55, 200)
- Plot (65, 230)
- Plot (75, 260)
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Connect the points with a smooth curve to create the ogive.
Step 4
Use the cumulative frequency graph to determine the median age of the people who attended the music concert.
Answer
To find the median using the cumulative frequency graph:
- The total number of people is 320, so the median is the value that corresponds to the 160th person (since median = 320 / 2).
- Locate 160 on the cumulative frequency scale of the graph and draw a horizontal line to intersect the ogive, then drop a vertical line down to the age axis.
- The age value at this intersection is the median age, which equals 41.