Math, asked by Dictator6822, 11 months ago

The following data is arranged in the ascending order4,5,8,11,5x,5x+2,16,18,21,22If the median of the data is 13, then find the value of x.​

Answers

Answered by Alcaa
0

The value of x is 2.4 .

Step-by-step explanation:

We are given the following data arranged in the ascending order below;

4, 5, 8, 11, 5x, 5x+2, 16, 18, 21, 22

Now, we are also provided with the median of this data and we have to find the value of x.

Now, how to perform the Calculation of Median;

Firstly, we will observe that the total number of observation (n) is even or odd.

  • If n is odd, the the formula for median is given by;

                 Median = (\frac{n+1}{2})^{th}  obs.

  • If n is even, then the formula for median is given by;

                 Median = \frac{(\frac{n}{2})^{th} \text{obs}  + (\frac{n}{2}+1) ^{th}  \text{obs}    }{2}    

Here, in our data we can see that n is even as n = 10.

So, Median is given by the formula;

                     Median = \frac{(\frac{n}{2})^{th} \text{obs}  + (\frac{n}{2}+1) ^{th}  \text{obs}    }{2}    

                            13   = \frac{(\frac{10}{2})^{th} \text{obs}  + (\frac{10}{2}+1) ^{th}  \text{obs}    }{2}

                            13   =  \frac{(5)^{th} \text{obs}  + (6) ^{th}  \text{obs}    }{2}

In our data 5^{th} and 6^{th} observation are 5x and  5x+2 respectively.

          So,             13  = \frac{5x + (5x+2)  }{2}

                             5x+5x+2 = 13 \times 2

                                    10x+2 = 26

                                    10x=24

                                     x=\frac{24}{10}=2.4

Therefore, the value of x in the above data is 2.4.​

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