Find Groups with Mean = 6: Average Value Selection Problem

Question

Choose the group of numbers of which 6 is the average.

Video Solution

Solution Steps

00:00 Choose the group with an average of 6
00:03 To calculate the average, we sum up and divide by the number of occurrences
00:10 We'll use the formula for calculating average to find the mean
00:15 This is the average, now let's move to the next group
00:18 We'll use the formula for calculating average to find the mean
00:25 This is the average, now let's move to the next group
00:30 In a group where all numbers are identical, the average is that number
00:35 This is the average, now let's move to the next group
00:39 We'll use the formula for calculating average to find the mean
00:47 This is the average
00:50 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will apply the formula for the average. We will proceed by evaluating each choice to identify which group has an average of 6.

The average for a group of numbers is calculated as:

Average=Sum of valuesNumber of values \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}

Now, let's calculate and analyze:

  • Choice 1: 1,2,31,2,3
    Calculate the sum: 1+2+3=61 + 2 + 3 = 6
    Number of values: 3
    Average: 63=2\frac{6}{3} = 2

  • Choice 2: 3,3,33,3,3
    Calculate the sum: 3+3+3=93 + 3 + 3 = 9
    Number of values: 3
    Average: 93=3\frac{9}{3} = 3

  • Choice 3: 6,0,06,0,0
    Calculate the sum: 6+0+0=66 + 0 + 0 = 6
    Number of values: 3
    Average: 63=2\frac{6}{3} = 2

  • Choice 4: 6,8,46,8,4
    Calculate the sum: 6+8+4=186 + 8 + 4 = 18
    Number of values: 3
    Average: 183=6\frac{18}{3} = 6

Thus, the group of numbers with an average of 6 is 6,8,46,8,4.

Answer

6,8,4 6,8,4