Question

The following numbers are arranged in ascending order. Their median is 11.
1, 2, 5, X-3, x + 1, x + 4, 15, 16, 19
(i) Find the value of x.
(ii) Hence, find their mean.​

Answer 1

Here's your answer!

Hope it helps!

Answer 2

Answer:

The value of x = 10

Mean of given data = 10

Step-by-step explanation:

Given data

⇒ 1, 2, 5, x-3, x+1, x+4, 15, 16, 19

⇒ the above data is arranged in ascending order

⇒ median of the data = 11

Here we need to find x value and mean of the given data

⇒ the number of observation in given data n = 9  

                                         [ here 9 is a odd number ]

⇒ if the number of observations of given data is odd number

then the formula for median = $[\frac{n+1}{2} ]$ th term of given data

⇒ the median of given data = $[\frac{9+1 }{2} ]$  = 10/ 2 = 5th term

⇒ median = 5th term of given data = x + 1

⇒ from given data median = 11  ⇒   x+ 1 =11

                                                          x = 10

⇒ The value of x = 10

⇒ the given data can be written as 1, 2,5,10-3,10+1,10+4,15,16,19

⇒  1, 2, 5, 7, 11, 14, 15, 16, 19

⇒ mean = sum of observations ÷ number of observations

              =  $\frac{1+2+ 5+7+11+14+15+16+19}{9}$  

              = 90/9 = 10

⇒ Mean of given data = 10