Question

find the median and mode of the following data. 28 ,15,40,25,16,28,32,36,42,16,19,23.



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Answer 1

Answer: The median of the data is 26.5 and the mode is 16 and 28.

Explanation:

The given data is,

28 ,15,40,25,16,28,32,36,42,16,19,23

Arrange the given data in either ascending order or descending order.

15,16,16,19,23,25,28,28,32,36,40,42

The total number of items is 12 which is an even number.

$\text{Median}=\frac{\frac{n}{2}\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}$

$\text{Median}=\frac{\frac{12}{2}\text{th term}+(\frac{12}{2}+1)\text{th term}}{2}$

$\text{Median}=\frac{6\text{th term}+7\text{th term}}{2}$

So the median is the average of 6th and 7th term.

The 6th and 7th terms are 25 and 28.

$\text{Median}=\frac{25+28}{2}$

$\text{Median}=26.5$

Therefore the median is 26.5.

Mode is the number which occurs most frequently.

Since 16 and 28 have highest frequency which is 2.

The function have two modes 16 and 28.

Answer 2

Mode = most occurring =28,16

Median = ascending order.

⇒15,16,16,19,23,25,28,28,32,36,40,42

Median =225+28=253=26.5.

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