Exam (elaborations)
STA1510 Exam pack 2024(Basic Statistics)
- Course
- Basic Statistics
- Institution
- University Of South Africa
STA1510 Exam pack 2024(Basic Statistics)
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STA1510 EXAM PACK2024
QUESTIONS AND
ANSWERS
FOR ASSISTANCE CONTACT
EMAIL:gabrielmusyoka940@gmail.com
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2018 EXAM QUESTIONS AND PROPOSED ANSWERS: Mostly from
QUESTION 1
The following stem–and–leaf display gives the scores of a sample of 30
students on a statistics exam
5: 0 2 7
6: 1 5 4 9 8
7: 1 2 2 5 2 6 7 9 9
8: 0 1 3 4 7 7 7
9: 6 8 2 3 2 5
Which statement is incorrect?
1. The median is equal to 78.
2. The mode is equal to 87:
3. 40% of the students scored above 80%
4. The range is equal to 48:
5. 10% of the students scored less than 60%
Answer
QUESTION 2
The following is a stem–and–leaf display representing the amount of Petrol
purchased, in litres.
4158
502259
61255667
703
Which one of the following statements is correct?
1. The range is 29.
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2. The mode is 65:
3. The fifth smallest value is 2:
4. The median is 61:
5. The mean, XN D 68:06:
[TURN OVER]
3 STA1510
OCT/NOV 2018
QUESTION 3
In perfectly symmetric distributions, which of the following is NOT a
correct statement?
1. The distance from Q1 to Q2 equals to the distance from Q2 to Q3.
2. The distance from the smallest observation to Q1 is the same as the
distance from Q3 to the largest observation.
3. The distance from the smallest observation to Q2 is the same as the
distance from Q2 to the largest observation.
4. The distance from Q1 to Q3 is half of the distance from the smallest to
the largest observation.
5. The mean is equal to the median.
The answer is 4
Why:
In a perfectly symmetric distribution:
- Q1 (first quartile) = 25th percentile
- Q2 (second quartile) = 50th percentile = Median
- Q3 (third quartile) = 75th percentile
The statements:
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1. True: Q2 is equidistant from Q1 and Q3.
2. True: The distance from the smallest observation to Q1 equals
the distance from Q3 to the largest observation (symmetry).
3. True: The distance from the smallest observation to Q2 equals
the distance from Q2 to the largest observation (symmetry).
4. False: The distance from Q1 to Q3 is actually equal to the
interquartile range (IQR), which is not necessarily half of the
distance from the smallest to the largest observation. The IQR
represents the middle 50% of the data.
5. True: In a symmetric distribution, the mean equals the median.
QUESTION 4
The figure below shows the histogram of the numeric frequency
distribution for shoppers’ ages.
20 _ < 30 _ < 40 _ < 50 _ < 60 _ < 70
Number of Shoppers Age intervals (in years)
How many shoppers are between 20 and 29 years of age?
Answer: 3 (6 shoppers)
1. 3 shoppers
2. 4 shoppers
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