Understanding Mean

The mean, or average, of a group of numbers is calculated by summing all the numbers in the group and then dividing the total sum by the count of numbers in the group.

The formula for the mean ($\bar{x}$) is:

$$\bar{x} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}$$

We need to calculate the mean for each of the given groups (A, B, C, and D) and then compare them to find the smallest one.

Calculating Means for Each Group

Mean of Group A

Group A: 1, 2, 3, 4, 5, 6, 7, 8, 9

Count of numbers in Group A = 9

Sum of numbers in Group A = $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$

Mean of Group A = $\frac{45}{9} = 5$

Mean of Group B

Group B: 1, 2, 3, 4, 6, 6, 7, 8, 9

Count of numbers in Group B = 9

Sum of numbers in Group B = $1 + 2 + 3 + 4 + 6 + 6 + 7 + 8 + 9 = 46$

Mean of Group B = $\frac{46}{9} \approx 5.11$

Mean of Group C

Group C: 1, 2, 2, 4, 5, 6, 7, 8, 9

Count of numbers in Group C = 9

Sum of numbers in Group C = $1 + 2 + 2 + 4 + 5 + 6 + 7 + 8 + 9 = 44$

Mean of Group C = $\frac{44}{9} \approx 4.89$

Mean of Group D

Group D: 1, 3, 3, 4, 5, 6, 7, 9, 9

Count of numbers in Group D = 9

Sum of numbers in Group D = $1 + 3 + 3 + 4 + 5 + 6 + 7 + 9 + 9 = 47$

Mean of Group D = $\frac{47}{9} \approx 5.22$

Comparing Means

Let's list the calculated means for each group:

• Mean of Group A: 5
• Mean of Group B: $\approx$ 5.11
• Mean of Group C: $\approx$ 4.89
• Mean of Group D: $\approx$ 5.22

Comparing these values, we can see which mean is the smallest:

$4.89$ (Group C) is smaller than $5$ (Group A), $5.11$ (Group B), and $5.22$ (Group D).

Therefore, Group C has the smallest mean.