Question

the following observations 40,42,45,x-1 x + 1, 54,51,62 are arranged in ascending order if the median is 49 find the value of x hence find the mean

Answer 1

x = 49 and mean of the numbers = 49

Step-by-step explanation:

Given numbers are 40, 42, 45, (x-1), (x+1), 54, 51 and 62 arranged in ascending order.

Median of these numbers is 49.

Here number of terms are 8 (even number) so the median of these terms will be = $\frac{\text{Sum of middle two terms}}{2}$

= $\frac{(x-1)+(x+1)}{2}$

= x

Therefore, x = 49

Now mean of these terms = $\frac{\text{Sum of all terms}}{\text{Number of terms}}$

= $\frac{40+42+45+48+50+54+51+62}{8}$

= 49

Therefore, mean of the given numbers is 49.

Learn more about the mean from https://brainly.in/question/6419111

Answer 2

Value of x is 49.

Mean is 49.    

Given

To find the value of x and mean.

Given observations are 40, 42, 45, x-1, x+1, 54, 51, 62.

Median is 49.

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

Where, n represents the number of observation in the given data.

            n = (40, 42, 45, x-1, x+1, 54, 51, 62)

               = 8

To find the value of x :

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

            = $\frac{\left(\frac{8}{2}\right)^{t h} \text { observation }+\left(\frac{8}{2}+1\right)^{t h} \text { observation }}{2}$

            = $\frac{(4)^{t h} \text { observation }+(5)^{t h} \text { observation }}{2}$

Here, $4^t^h$ observation is (x-1).

         $5^t^h$ observation is (x+1).

         Median = 49.

         Median = $\frac{(4)^{t h} \text { observation }+(5)^{t h} \text { observation }}{2}$

                  49 = $\frac{(x-1)+(x+1)}{2}$

                  49 = $\frac{x-1+x+1}{2}$

                  49 = $\frac{2x}{2}$

                  x = 49.      

Hence, the value of x is 49.

$4^t^h$ observation = x - 1 = 49 - 1 = 48

$5^t^h$ observation = x + 1 = 49 + 1 = 50

To find the mean :

                             40, 42, 45, x-1, x+1, 54, 51, 62.

                             40, 42, 45, (49-1), (49+1), 54, 51, 62.

                             40, 42, 45, 49, 50, 54, 51, 62.

                  Mean = $\frac{\text { Sum of obsevation }}{\text { Number of observation }}$

                            = $\frac{40+42+45+49+50+54+51+62}{8}$

                            = $\frac{392}{8}$  

                  Mean = 49

To learn more...

1. brainly.in/question/14271177

2. brainly.in/question/6419111