The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below. COMMISSION EARNED (IN THOUSANDS OF RANDS) FREQUENCY 20 < x ≤ 40 7 40 < x ≤ 60 6 60 < x ≤ 80 8 80 < x ≤ 100 10 100 < x ≤ 120 4 2.1 Write down the modal class of the data. 2.2 Complete the cumulative frequency column in the table given in the ANSWER BOOK. 2.3 Draw an ogive (cumulative frequency curve) to represent the data on the grid provided in the ANSWER BOOK. 2.4 A salesman receives a bonus if his commission is more than R90 000 for the month. Calculate how many of the salesmen received bonuses for this month. 2.5 Determine the approximate mean commission earned by the salesmen in this month correct to the nearest thousand rand.

NSC Mathematics Statistics: The commission earned, in thousa

The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below - NSC Mathematics - Question 2 - 2017 - Paper 2

Question 2

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The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below. COMMISSION EARNED (IN THOUSAND... show full transcript

Worked Solution & Example Answer:The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below - NSC Mathematics - Question 2 - 2017 - Paper 2

Step 1

2.1 Write down the modal class of the data.

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Answer

The modal class is the class with the highest frequency. From the table, the class '80 < x ≤ 100' has the highest frequency of 10. Thus, the modal class is 80 < x ≤ 100.

Step 2

2.2 Complete the cumulative frequency column in the table given in the ANSWER BOOK.

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Answer

To complete the cumulative frequency, we add the frequency of each class to the cumulative frequency of the previous class:

For 20 < x ≤ 40: Cumulative Frequency = 7
For 40 < x ≤ 60: Cumulative Frequency = 7 + 6 = 13
For 60 < x ≤ 80: Cumulative Frequency = 13 + 8 = 21
For 80 < x ≤ 100: Cumulative Frequency = 21 + 10 = 31
For 100 < x ≤ 120: Cumulative Frequency = 31 + 4 = 35

The completed cumulative frequency table is:

COMMISSION EARNED FREQUENCY CUMULATIVE FREQUENCY 20 < x ≤ 40 7 7 40 < x ≤ 60 6 13 60 < x ≤ 80 8 21 80 < x ≤ 100 10 31 100 < x ≤ 120 4 35

Step 3

2.3 Draw an ogive (cumulative frequency curve) to represent the data on the grid provided in the ANSWER BOOK.

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Answer

To draw the ogive, plot the cumulative frequencies against the upper class boundaries:

(40, 7)
(60, 13)
(80, 21)
(100, 31)
(120, 35)

Connect these points with a smooth curve to create the ogive.

Step 4

2.4 A salesman receives a bonus if his commission is more than R90 000 for the month. Calculate how many of the salesmen received bonuses for this month.

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Answer

A commission of more than R90 000 corresponds to more than 90 in thousands of rands. From the cumulative frequency, those in the class '100 < x ≤ 120' (with a frequency of 4) received bonuses. Thus, 4 salesmen received bonuses.

Step 5

2.5 Determine the approximate mean commission earned by the salesmen in this month correct to the nearest thousand rand.

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Answer

To find the approximate mean, we use the midpoint of each class:

Midpoint for 20 < x ≤ 40 = 30
Midpoint for 40 < x ≤ 60 = 50
Midpoint for 60 < x ≤ 80 = 70
Midpoint for 80 < x ≤ 100 = 90
Midpoint for 100 < x ≤ 120 = 110

Then we calculate:
Mean = ( \frac{(30 \times 7) + (50 \times 6) + (70 \times 8) + (90 \times 10) + (110 \times 4)}{35} )
Mean = ( \frac{(210 + 300 + 560 + 900 + 440)}{35} = \frac{2410}{35} \approx 68.86 )
Thus, the approximate mean commission earned is R69 000 when rounded to the nearest thousand rand.

The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below - NSC Mathematics - Question 2 - 2017 - Paper 2

Worked Solution & Example Answer:The commission earned, in thousands of rands, by the salesmen of a particular company in a certain month is shown in the table below - NSC Mathematics - Question 2 - 2017 - Paper 2

2.1 Write down the modal class of the data.

2.2 Complete the cumulative frequency column in the table given in the ANSWER BOOK.

2.3 Draw an ogive (cumulative frequency curve) to represent the data on the grid provided in the ANSWER BOOK.

2.4 A salesman receives a bonus if his commission is more than R90 000 for the month. Calculate how many of the salesmen received bonuses for this month.

2.5 Determine the approximate mean commission earned by the salesmen in this month correct to the nearest thousand rand.

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