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  • Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Answers (1)

Answer : 20

Here, the observations are :

6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43

To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.

The terms are already given in ascending order so we have to find the middle term.

Number of terms, n=10(even)

\text{So, Median = average of}\left ( \frac{n}{2} \right )^{th} \text{ and}\left ( \frac{n}{2} +1\right )^{th}\text{term}

\Rightarrow Median =24            (given)

\text{Median}=\frac{\left ( \frac{n}{2} \right )^{th}\text {observation}+\left ( \frac{n}{2}+1 \right )^{th}\text {observation}}{2}

24=\frac{\left ( \frac{10}{2} \right )^{th}\text {obs.}+\left ( \frac{10}{2}+1 \right )\text {obs.}}{2}

24=\frac{5^{th}\text {obs.}+6^{th}\text {obs.}}{2}

24=\frac{x+1+2x-13}{2}

\Rightarrow 2 \times 24=x+1+2x-13

\Rightarrow 48=3x-12

\Rightarrow 48+12=3x

\Rightarrow 60=3x

\Rightarrow x=20

Hence, the correct answer is 20.

Posted by

infoexpert23

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