The mean of 6 pieces of data is 7. Five of the data values are 9, 4, 8, 8, and 7. What is the sixth data value?

Question

asked Feb 13, 2024 63.1k views

1 Answer

Jhoana · Answer 1 · 2024-02-17T02:47:37+0000

$\:\:\:\:\:\:\longrightarrow \sf \underline{Mean = (Sum\: of \: Observations )/(No.\:of \:Observations )}\\$

As per question, we are given -

The mean of 6 pieces of data is 7 which states the no of observations is 6. Let the 6th datum be x.Then, the sum of observations will be -

$\:\:\:\:\:\:\star\:\sf Sum \:of \:observations \\$

$\:\:\:\:\:\:\longrightarrow \sf 9+4+8+8+7+x \\$

$\:\:\:\:\:\:\longrightarrow \sf 36+x \\$

Now that, we are given all the values which are required for solving this problem, so we can substitute the values and solve for the sixth datum -

$\:\:\:\:\:\:\longrightarrow \sf Mean = (Sum\: of \: Observation )/(No.\:of \:Observation )\\$

$\:\:\:\:\:\:\longrightarrow \sf 7 = (36+x)/(6)\\$

$\:\:\:\:\:\:\longrightarrow \sf 7* 6 = 36+x \\$

$\:\:\:\:\:\:\longrightarrow \sf 42 -36 =x\\$

$\:\:\:\:\:\:\longrightarrow \sf \underline{x = 6}\\$