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In an experiment, a group of 23 girls were presented with a page containing 30 coloured rectangles - NSC Mathematics - Question 2 - 2017 - Paper 2
Question 2
In an experiment, a group of 23 girls were presented with a page containing 30 coloured rectangles. They were asked to name the colours of the rectangles correctly a... show full transcript
Worked Solution & Example Answer:In an experiment, a group of 23 girls were presented with a page containing 30 coloured rectangles - NSC Mathematics - Question 2 - 2017 - Paper 2
Step 1
Step 2
2.1.2 The interquartile range of the data
Answer
To find the interquartile range (IQR), we first need to find Q1 and Q3:
- Q1 (1st quartile) is the median of the first half of the data, while Q3 (3rd quartile) is the median of the second half.
- In this case, Q1 = 16 and Q3 = 24.
Thus, the IQR is calculated as:
Step 3
2.2 The standard deviation of the times taken by the girls is 5.94. How many girls took longer than ONE standard deviation from the mean to name the colours?
Answer
Given that the mean is 20.52 and the standard deviation is 5.94, we find:
Now we determine how many times are greater than 26.46 seconds:
- The relevant times are 28, 28, and 36.
In total, 4 girls took longer than ONE standard deviation from the mean.
Step 4
2.3 Draw a box and whisker diagram to represent the data on the number line provided in the ANSWER BOOK.
Answer
The box and whisker diagram will use the five-number summary:
- Minimum: 12
- Q1: 16
- Median: 20
- Q3: 24
- Maximum: 36
This will yield a visual representation where the box spans from Q1 to Q3, with whiskers extending to the minimum and maximum values.
Step 5
2.4.1 Which of the two groups, girls or boys, had the lower median time to correctly name the colours of the rectangles?
Answer
From the boys' five-number summary, the median is 23. In contrast, the girls' median (from the sorted data) is 20.52 seconds. Therefore, the girls had a lower median time.
Step 6
2.4.2 The first three learners who named the colours of all 30 rectangles correctly in the shortest time will receive a prize. How many boys will be among these three prizewinners? Motivate your answer.
Answer
Since 5 boys completed the task in less than 15 seconds, which is the minimum time recorded for the boys, there can be 3 prizewinners from this group. Therefore, the possibility exists that all three prizewinners could be boys, depending on their completion times.