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, 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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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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What is the mean of the range, mode and median of the data given below...

Mean:
To find the mean, we need to add up all the numbers in the given data set and then divide by the total number of values.

5 + 10 + 3 + 6 + 4 + 8 + 9 + 3 + 15 + 2 + 9 + 4 + 19 + 11 + 4 = 112

There are 15 numbers in the data set, so the mean is 112/15 = 7.47 (rounded to two decimal places).

Mode:
The mode is the value that appears most frequently in the data set. In this case, the number 4 appears three times, which is more than any other number. Therefore, the mode of the data set is 4.

Median:
The median is the middle value when the data set is arranged in ascending order. To find the median, we first need to arrange the numbers in ascending order:

2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19

Since there are 15 numbers, the middle value is the 8th number, which is 6. Therefore, the median of the data set is 6.

Mean of the range:
The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 19 and the lowest value is 2. Therefore, the range is 19 - 2 = 17.

To find the mean of the range, we divide the range by 2:

17/2 = 8.5

Therefore, the mean of the range is 8.5.

Conclusion:
The mean of the data set is 7.47, the mode is 4, the median is 6, and the mean of the range is 8.5. Therefore, the correct answer is option 'D' - 9.

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