Question

Compare mean and median for the data 5,15,20,25,30 have relation *

B)mean>median

A)mean<median

D)none of these

C) mean=median​

Answer 1

Answer:

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mean<median

Answer 2

⇒ Final Answer:

Option A: mean < median

⇒ Given:

The data - 5, 15, 20, 25, 30

⇒ To Find:

The comparison of the mean and the median of the data

⇒ Formulae to be used:

→ $\boxed{\sf{Mean=\dfrac{Sum\:of\:all\:values}{Total\:no.\:of\:values}}}$

→ $\boxed{\sf{Median=Middle\:most\:value}}$

⇒ Solution:

First, we can calculate the mean of the given data.

The data is 5, 15, 20, 25 and 30. This data is already in ascending order.

Formula to find mean:

$\sf{Mean=\dfrac{Sum\:of\:all\:values}{No.\:of\:values}}$

Sum of all values = 5 + 15 + 20 + 25 + 30 = 95

No. of values = 5

$\sf{Mean=\dfrac{5+15+20+25+30}{5}}$

$\sf{Mean=\dfrac{95}{5}}$

$\sf{Mean=19}$

∴ The mean of the data is 19.

Now, we can calculate the median of the data.

The data is already in ascending order and we know that the median is the middlemost value in the data.

The total no. of values is 5, which is odd.

Nearest even number = 4

$\sf{\dfrac{4}{2}=2}$

Hence we have to take 2 values from the right end and 2 values from the left end.

5, 15, 20, 25, 30

5 and 15 are from the left end and 25 and 30 are from the right end.

We can see that, we are left with the number 20.

∴ The median of the data is 20.

Comparison:

Mean of the data = 19

Median of the data = 20

19 < 20

Mean < Median

Hence, the required option is Option A: mean < median.

Measures of Central Tendency

The three basic measures of central tendency are stated below:

 → Mean

Mean is the standard name given to the average of numbers. It helps to take the average of a given data. To find the mean, we have to divide the no. of values from the sum of the values in the data.

Formula:

$\sf{Mean=\dfrac{Sum\:of\:values}{No.\:of\:values}}$

 → Median

Median refers to the middle most value of the data when arranged in ascending/descending order.

Formula:

$\sf{Median\:for\:even\:no.\:of\:values=\dfrac{Sum\:of\:two\:middle\:values}{2}}$

$\sf{Median\:for\:odd\:no.\:of\:values=Middle\:value\:of\:the\:arranged\:data}$

 → Mode

The value of the data with highest frequency is known as mode. That is, the number that occurs the maximum number of times is known as the mode of the data.

No specific formula for mode.