For what value of $x$ , the mode of the following data is $5$ ?
$1, 2, 5, 7, 5, 2, 7, 5, 9, 2, 3, x, 11$

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Solution

Find the value of $x$
The given data set is: $1, 2, 5, 7, 5, 2, 7, 5, 9, 2, 3, x, 11$
The frequency distribution table is as follows.
NUMBER FREQUENCY
$1$ $1$
$2$ $3$
$3$ $1$
$5$ $3$
$7$ $2$
$9$ $1$
$11$ $1$
$X$ $1$
As we see from the table, both $2$ and $5$ can be mode, but according to the question, $5$ is the mode.
So, number of occurrences of $5$ should be more than that of $2$ .
$2$ and $5$ both occur $3$ times, but $5$ should have higher frequency. Hence, $x$ can be $5$ .
Hence, the value of $x$ is $5$ .

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