Question

What value added to the set below would give a mean of 33?

{19, 27, 64, 36}
19

30

27

42

Answer 1

Answer is 19

If you add all of the numbers together including 19. You would get 165, then divide the total by 5. Your answer would be 33!

Answer 2

Answer:

19

Step-by-step explanation:

Given:

• data = [19,27,64,36]

• mean value = 33

To find:

• another data / last data

Therefore:

• New data is 19,27,64,36,x
• Where x is an unknown value/data.

Mean Value:

$\displaystyle \large{m=\dfrac{1}{n}\sum_{i =1}^n x_i \to \dfrac{x_1+x_2+x_3+...+x_n}{n}}$

• m = mean value
• x1+x2+x3+...+xn = sum of all data
• n = amount of data

Therefore:

$\displaystyle \large{33=\dfrac{19+27+64+36+x}{5}}$

Solve for x - first, multiply both sides by 5 to clear out the denominator:

$\displaystyle \large{33\cdot 5=\dfrac{19+27+64+36+x}{5} \cdot 5}\\\displaystyle \large{165=19+27+64+36+x}$

Evaluate the sum:

$\displaystyle \large{165=146+x}$

Subtract both sides by 146:

$\displaystyle \large{165-146=146-146+x}\\\displaystyle \large{19=x}$

Therefore, another value/data that will give a mean value of 33 is 19.