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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?
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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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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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