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The table below shows the mass (in kg) of the school bags of 80 learners - NSC Mathematics - Question 1 - 2022 - Paper 2
Question 1
The table below shows the mass (in kg) of the school bags of 80 learners. | MASS (in kg) | FREQUENCY | |--------------|-----------| | 5 < m ≤ 7 | 6 | | 7 ... show full transcript
Worked Solution & Example Answer:The table below shows the mass (in kg) of the school bags of 80 learners - NSC Mathematics - Question 1 - 2022 - Paper 2
Step 1
Step 2
1.2 Complete the cumulative frequency column in the table in the ANSWER BOOK.
Answer
The cumulative frequency is calculated by adding the frequency values. The cumulative frequency table is as follows:
| MASS (in kg) | FREQUENCY | CUMULATIVE FREQUENCY |
|---|---|---|
| 5 < m ≤ 7 | 6 | 6 |
| 7 < m ≤ 9 | 18 | 24 |
| 9 < m ≤ 11 | 21 | 45 |
| 11 < m ≤ 13 | 19 | 64 |
| 13 < m ≤ 15 | 11 | 75 |
| 15 < m ≤ 17 | 4 | 79 |
| 17 < m ≤ 19 | 1 | 80 |
Step 3
1.3 Draw a cumulative frequency graph (ogive) for the given data on the grid provided in the ANSWER BOOK.
Answer
To draw the cumulative frequency graph, plot the cumulative frequency values against the upper limits of the classes. Connect the points with a smooth curve. Ensure that the x-axis represents the mass in kg and the y-axis represents the cumulative frequency.
Step 4
1.4 Use the graph to determine the median mass for this data.
Answer
To find the median mass using the graph, locate the point corresponding to 40 (half of 80) on the cumulative frequency axis. Drop a vertical line to intersect the cumulative frequency curve and then drop a horizontal line to the x-axis to read the median mass, which is 10.5 kg.
Step 5
1.5.1 Calculate the estimated mean mass of the school bags.
Answer
To calculate the estimated mean, use the midpoints of each class interval multiplied by their respective frequencies:
ar{x} = \frac{(6 \times 6) + (8 \times 18) + (10 \times 21) + (12 \times 19) + (14 \times 11) + (16 \times 4) + (18 \times 1)}{80}
Calculating this gives:
ar{x} = \frac{854}{80} = 10.68 \text{ kg}
Step 6
1.5.2 The mean mass of this group of learners was found to be 80 kg. On average, are these school bags satisfying the international guideline with regard to mass? Motivate your answer.
Answer
According to the international guideline, the mass of a school bag should not exceed 10% of a learner's body mass. Hence, for a mean body mass of 80 kg:
Since the estimated mean mass of the school bags is 10.68 kg, which exceeds 8 kg, we conclude that, on average, the school bags do not satisfy the international guideline.