Sample Size, and Sum of a Data Set

Introduction

In this lesson, we solve problems involving, the sample size, sum of a data set and its mean. Any two of these three quantities are given and we find the third unknown quantity using the relation between these 3 quantities.

Formula

• Mean=SumofthedataNumberofdata
• Sum of the data = Mean Number of data
• Numberofdata=SumofthedataMean

Example 1

The average of x and 3 is equal to the average of x, 6 and 9. Find x

1, 1, 4, 4, 5, 6, 7, 7, 10, 10

Solution

Step 1:

Average of x and 3 = (x+3)2

Average of x, 6, and 9 = (x+6+9)3

Step 2:

Given (x+3)2=(x+15)3

Solving we get 3x + 9 = 2x + 30 or

3x 2x = x = 30 9 = 21

Step 3:

So x = 21

Example 2

7 consecutive even integers have an average of 48. Find the average of the greatest two of those integers.

Solution

Step 1:

Let the consecutive even integers be

x 6, x 4, x 2, x, x + 2, x + 4, x + 6

Their average = (x6+x4+x2+x+x+2+x+4+x+6)7=7×7 = 48. So X=48

Step 2:

So the numbers are 42, 44, 46, 48, 50, 52, 54

The average of the two greatest of these integers 52 and 54 is 52+54/2 = 53