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At a certain school, the staff committee wanted to determine how many glasses of water the staff members drank during a school day - NSC Mathematics - Question 2 - 2023 - Paper 2
Question 2
At a certain school, the staff committee wanted to determine how many glasses of water the staff members drank during a school day. All teachers present on a specifi... show full transcript
Worked Solution & Example Answer:At a certain school, the staff committee wanted to determine how many glasses of water the staff members drank during a school day - NSC Mathematics - Question 2 - 2023 - Paper 2
Step 1
Complete the cumulative frequency column provided in the table in the ANSWER BOOK.
Answer
To complete the cumulative frequency table, add the number of staff members in each category:
- For 0 ≤ x < 2: Cumulative frequency = 5
- For 2 ≤ x < 4: Cumulative frequency = 5 + 15 = 20
- For 4 ≤ x < 6: Cumulative frequency = 20 + 13 = 33
- For 6 ≤ x < 8: Cumulative frequency = 33 + 5 = 38
- For 8 ≤ x < 10: Cumulative frequency = 38 + 2 = 40
Complete table:
NUMBER OF GLASSES OF WATER DRANK PER DAY | CUMULATIVE FREQUENCY 0 ≤ x < 2 | 5 2 ≤ x < 4 | 20 4 ≤ x < 6 | 33 6 ≤ x < 8 | 38 8 ≤ x < 10 | 40
Step 2
Step 3
How many staff members drank fewer than 6 glasses of water during a school day?
Answer
To find how many staff members drank fewer than 6 glasses of water, add the categories for 0 ≤ x < 2 and 2 ≤ x < 4 and 4 ≤ x < 6:
Number of staff members = 5 + 15 + 13 = 33 staff members drank fewer than 6 glasses of water.
Step 4
How many teachers were absent on the day of the interviews?
Answer
Let the mean of the k absent teachers be expressed as:
ar{x} = \frac{(1 \times \frac{k}{2}) + (3 \times 15) + (5 \times (13 + \frac{k}{2})) + (7 \times 5) + (9 \times 2)}{40 + k} = 4
Substituting the values:
Solving gives:
Thus, 8 teachers were absent on the day of the interviews.