Question

i.Find the mean of the following sets of numbers:
a. 2.5, 2.4, 3.5, 2.8, 2.9, 3.3, 3.6
b. -6, -2, -1, 0, 1, 2, 5, 9
ii.The mean of the numbers 6, y, 7, x, 14 is 8. Express y in the terms of x.

Answer 1

Hint: In first part of this question add all the numbers together and then we will divide it by the total number of number that were added and in the second part of the question the mean is already given so we will add up the given numbers including x and y and then we will divide it with total numbers that were added and then we will find the relation between x and the y.

Complete step-by-step answer:
Part (i)
a.Given the set of the numbers \[2.5,2.4,3.5,2.8,2.9,3.3,3.6\]
So the sum of these given number will be \[2.5 + 2.4 + 3.5 + 2.8 + 2.9 + 3.3 + 3.6 = 21\]
Now since there are a total of 7 numbers whose mean is to be find, so the mean of the given number will be
\[
\Rightarrow Mean = \dfrac{{21}}{7} \\
   = 3 \;
 \]
Hence the mean of the numbers \[2.5,2.4,3.5,2.8,2.9,3.3,3.6 = 3\]
b.Given the set of the numbers \[ - 6, - 2, - 1,0,1,2,5,9\]
So the sum of these given number will be \[ - 6 - 2 - 1 + 0 + 1 + 2 + 5 + 9 = 8\]
Now since there are a total of 8 numbers whose mean is to be find, so the mean of the given number will be
\[
\Rightarrow Mean = \dfrac{8}{8} \\
   = 1 \;
 \]
Hence the mean of the numbers \[ - 6, - 2, - 1,0,1,2,5,9 = 1\]
Part (ii)
Given the set of the numbers \[6,y,7,x,14\]
In this part of the question since mean is already given and data is missing so first we will find the sum of data in term of x and y
So the sum of these given number will be \[6 + y + 7 + x + 14 = 27 + x + y\]
Now since there are a total of 5 numbers whose mean is given, hence we can write xx and y
\[
\Rightarrow Mean = \dfrac{{27 + x + y}}{5} \\
\Rightarrow 8 = \dfrac{{27 + x + y}}{5} \\
\Rightarrow 27 + x + y = 40 \\
\Rightarrow x + y = 13 \;
 \]
Hence we can further write the obtained equation as y in the terms of x as
 \[
  x + y = 13 \\
\Rightarrow y = 13 - x \;
 \]

Note: Mean is the average of the set of numbers. To find the mean of the numbers add up all the numbers and divide it with how many numbers were added. Students must note that to find the missing numbers of the given set of data we must know the mean for that given numbers.