To complete the frequency table, we first need to categorize the given marks of 30 learners into the specified age intervals. Let's break down the marks according to the intervals:
Marks:
- 52, 88, 85, 75, 72, 42, 58, 56, 33, 45
- 36, 89, 42, 55, 66, 63, 68, 69, 35, 89
- 52, 72, 72, 66, 55, 56, 89, 75, 72, 32
Intervals:
- 30 ≤ 𝑥 < 40
- 40 ≤ 𝑥 < 50
- 50 ≤ 𝑥 < 60
- 60 ≤ 𝑥 < 70
- 70 ≤ 𝑥 < 80
- 80 ≤ 𝑥 < 90
Step 1: Count the frequency for each interval
- 30 ≤ 𝑥 < 40: 33, 36, 35, 32 (4 marks)
- 40 ≤ 𝑥 < 50: 42, 42, 45 (3 marks)
- 50 ≤ 𝑥 < 60: 52, 58, 56, 55, 52, 56, 55 (7 marks)
- 60 ≤ 𝑥 < 70: 66, 63, 68, 69, 66 (5 marks)
- 70 ≤ 𝑥 < 80: 75, 72, 72, 72, 75 (5 marks)
- 80 ≤ 𝑥 < 90: 88, 85, 89, 89, 89 (5 marks)
Completed Frequency Table
| Age Intervals | Tally | Frequency | |------------------|------------|-----------| | 30 ≤ x < 40 | |||| | 4 | | 40 ≤ x < 50 | ||| | 3 | | 50 ≤ x < 60 | ||||||| | 7 | | 60 ≤ x < 70 | ||||| | 5 | | 70 ≤ x < 80 | ||||| | 5 | | 80 ≤ x < 90 | ||||| | 5 | | Total | | 30 |
Step 2: Draw histogram
To draw the histogram, we can plot the frequency on the vertical (y-axis) and the age intervals on the horizontal (x-axis).
-
X-axis (Intervals):
- 30-39
- 40-49
- 50-59
- 60-69
- 70-79
- 80-89
-
Y-axis (Frequency):
- Ranges from 0 to the highest frequency observed, which is 7.
Histogram Data
- 30-39: 4
- 40-49: 3
- 50-59: 7
- 60-69: 5
- 70-79: 5
- 80-89: 5
Drawing the Histogram
To plot the histogram:
- Draw the x-axis and label it with the intervals.
- Draw the y-axis and label the frequency.
- Use bars to represent the frequency for each interval:
- Height of the bar for 30-39: 4
- Height of the bar for 40-49: 3
- Height of the bar for 50-59: 7
- Height of the bar for 60-69: 5
- Height of the bar for 70-79: 5
- Height of the bar for 80-89: 5
Conclusion
Now you have a completed frequency table and the instructions to draw the histogram based on the given data. If you'd like, you can use graphing software or paper to sketch the histogram based on the provided data points.
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