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What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?
- a)17
- b)16
- c)12.75
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Finding the First Quartile
To find the first quartile of a set of observations, we need to arrange the observations in order from smallest to largest and then divide the data set into four equal parts. The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest of the data.
Solution
Arranging the given observations in ascending order, we get:
10, 12, 15, 16, 18, 20, 23, 28
To divide the data set into four equal parts, we need to find the median (middle value) of the lower half of the data set. Since there are an even number of observations (8), we take the average of the two middle values: 15 and 16.
The median of the lower half of the data is (15 + 16) / 2 = 15.5.
To find the first quartile, we take the median of the observations that are less than or equal to 15.5. These observations are: 10, 12, 15, and 16. Taking the median of these values, we get:
Q1 = (12 + 15) / 2 = 13.5
Therefore, the first quartile for the given observations is 13.5. The correct option is (C) 12.75, which is close to but not exactly equal to the correct answer.
To find the first quartile of a set of observations, we need to arrange the observations in order from smallest to largest and then divide the data set into four equal parts. The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest of the data.
Solution
Arranging the given observations in ascending order, we get:
10, 12, 15, 16, 18, 20, 23, 28
To divide the data set into four equal parts, we need to find the median (middle value) of the lower half of the data set. Since there are an even number of observations (8), we take the average of the two middle values: 15 and 16.
The median of the lower half of the data is (15 + 16) / 2 = 15.5.
To find the first quartile, we take the median of the observations that are less than or equal to 15.5. These observations are: 10, 12, 15, and 16. Taking the median of these values, we get:
Q1 = (12 + 15) / 2 = 13.5
Therefore, the first quartile for the given observations is 13.5. The correct option is (C) 12.75, which is close to but not exactly equal to the correct answer.
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What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?a)17b)16c)12.75d)12Correct answer is option 'C'. Can you explain this answer?
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What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?a)17b)16c)12.75d)12Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?a)17b)16c)12.75d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?a)17b)16c)12.75d)12Correct answer is option 'C'. Can you explain this answer?.
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