Find the value of x, if the mode of the following data is $25$ .
$25, 20, 25, 18, 14, 15, 18, 16, 20, 25, 20, x, 18$

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Solution

The frequency table of the given data is as given below:
Value ( $x_{i}$ ): 14 15 16 18 20 25 x
Frequency ( $f_{i}$ ): 1 3 1 3 3 3 1
It is given that the mode of the given data is $25$ . So, it must have the maximum frequency. That is possible only when $x = 25$ .
Hence. $x = 25$ .

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If the mean of the data 3,21, 25, 17, (x+ 3), 19, (x- 4) is 18, find the value of x. Using this value of x, find the mode of the data.

For what value of x is the mode of the data 24, 15, 90, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.

20.6

p

$x$	$10$	$15$	$p$	$25$	$35$
$f$	$3$	$10$	$25$	$7$	$5$

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Value ( $x_{i}$ ):	14	15	16	18	20	25	x
Frequency ( $f_{i}$ ):	1	3	1	3	3	3	1