Question

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?​

Answer 1

`\:\:\:\:\:\:\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}\\`

• Therefore, the sixth datum is 6.