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What is the mean of the range, mode and median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
- a)10
- b)12
- c)8
- d)9
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the mean of the range, mode and median of the data given below...
Given:
The given data is 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
Concept used:
The mode is the value that appears most frequently in a data set
At the time of finding Median
First, arrange the given data in the ascending order and then find the term
Formula used:
Mean = Sum of all the terms/Total number of terms
Median = {(n + 1)/2}th term when n is odd
Median = 1/2[(n/2)th term + {(n/2) + 1}th] term when n is even
Range = Maximum value – Minimum value
Calculation:
Arranging the given data in ascending order
2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
Here, Most frequent data is 4 so
Mode = 4
Total terms in the given data, (n) = 15 (It is odd)
Median = {(n + 1)/2}th term when n is odd
⇒ {(15 + 1)/2}th term
⇒ (8)th term
⇒ 6
Now, Range = Maximum value – Minimum value
⇒ 19 – 2 = 17
Mean of Range, Mode and median = (Range + Mode + Median)/3
⇒ (17 + 4 + 6)/3
⇒ 27/3 = 9
∴ The mean of the Range, Mode and Median is 9
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Community Answer
What is the mean of the range, mode and median of the data given below...
Step 1: Calculate the Range
- Definition: The range is the difference between the maximum and minimum values in a dataset.
- Data: 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
- Max Value: 19
- Min Value: 2
- Calculation: Range = Max - Min = 19 - 2 = 17
Step 2: Calculate the Mode
- Definition: The mode is the number that appears most frequently in the dataset.
- Frequency Count:
- 2: 1 time
- 3: 2 times
- 4: 3 times
- 5: 1 time
- 6: 1 time
- 8: 1 time
- 9: 2 times
- 10: 1 time
- 11: 1 time
- 15: 1 time
- 19: 1 time
- Most Frequent: 4 (occurs 3 times)
Step 3: Calculate the Median
- Definition: The median is the middle value when the data is arranged in ascending order.
- Sorted Data: 2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
- Middle Value: With 15 values, the median is the 8th value.
- Median: 6
Step 4: Calculate the Mean of Range, Mode, and Median
- Values: Range = 17, Mode = 4, Median = 6
- Calculation: Mean = (Range + Mode + Median) / 3 = (17 + 4 + 6) / 3 = 27 / 3 = 9
Conclusion
- The mean of the range, mode, and median is 9, which confirms that the correct answer is option 'D'.
- Definition: The range is the difference between the maximum and minimum values in a dataset.
- Data: 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
- Max Value: 19
- Min Value: 2
- Calculation: Range = Max - Min = 19 - 2 = 17
Step 2: Calculate the Mode
- Definition: The mode is the number that appears most frequently in the dataset.
- Frequency Count:
- 2: 1 time
- 3: 2 times
- 4: 3 times
- 5: 1 time
- 6: 1 time
- 8: 1 time
- 9: 2 times
- 10: 1 time
- 11: 1 time
- 15: 1 time
- 19: 1 time
- Most Frequent: 4 (occurs 3 times)
Step 3: Calculate the Median
- Definition: The median is the middle value when the data is arranged in ascending order.
- Sorted Data: 2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
- Middle Value: With 15 values, the median is the 8th value.
- Median: 6
Step 4: Calculate the Mean of Range, Mode, and Median
- Values: Range = 17, Mode = 4, Median = 6
- Calculation: Mean = (Range + Mode + Median) / 3 = (17 + 4 + 6) / 3 = 27 / 3 = 9
Conclusion
- The mean of the range, mode, and median is 9, which confirms that the correct answer is option 'D'.
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What is the mean of the range, mode and median of the data given below?5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4a)10b)12c)8d)9Correct answer is option 'D'. Can you explain this answer?
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What is the mean of the range, mode and median of the data given below?5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4a)10b)12c)8d)9Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the mean of the range, mode and median of the data given below?5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4a)10b)12c)8d)9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the mean of the range, mode and median of the data given below?5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4a)10b)12c)8d)9Correct answer is option 'D'. Can you explain this answer?.
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