Question

5. If the mean of the data 3, 21, 25, 17, (x+3), 19, (x – 4) is 18, find the value
of x. Using this value of x, find the mode of the data.
​

Answer 1

Given: Observations; mean being 18.

To find: The value of x and then the mode.

Answer:

Mean is the average of all the observations.

Observations: 3, 21, 25, 17, (x + 3), 19 and(x - 4).

Total number of observations: 7.

Formula to find the mean:

$\tt Mean\ =\ \dfrac{Sum\ of\ all\ observations}{Total\ number\ of\ observations}$

Using the values we have in this formula,

$\tt 18\ =\ \dfrac{3\ +\ 21\ +\ 25\ +\ 17\ +\ x\ +\ 3\ +\ 19\ +\ x\ -\ 4}{7}\\\\\\126\ =\ 84\ +\ 2x\\\\\\126\ -\ 84\ =\ 2x\\\\\\42\ =\ 2x\\\\\\21\ =\ x$

We now have the value of x. Therefore, the observations are:

3, 21, 25, 17, 24, 19 and 17.

Mode is the most repeated observation.

From what we have, it's clear that 17 is repeated the most (two times.)

Hence, 17 is the mode.

Answer 2

3+21+25+17+19+(x+3)+(x-4) = 84+2x

no. of observations = 7

mean = 18

so, 84+2x/ 7 = 18

     2x= 18*7 - 84

    => x = 42/2 = 21

 mode is the most repeated observation

x+3 = 24

x-4 = 17

hence the mode is 17

hope it helps you ^_^