Question

a data set has the following values: 5,7,9,11,13. what is the mean of this data set?
a. 10
b. 8
c. 9
d. 11

Explanation:

Step1: Recall the formula for the mean

The mean (average) of a data set is calculated by the formula $\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n}$, where $\sum_{i = 1}^{n} x_{i}$ is the sum of all the data points and $n$ is the number of data points.

Step2: Calculate the sum of the data set

The data set is $5, 7, 9, 11, 13$. So, $\sum_{i = 1}^{5} x_{i}=5 + 7+9 + 11+13$. Let's calculate that: $5+7 = 12$, $12 + 9=21$, $21+11 = 32$, $32+13 = 45$.

Step3: Determine the number of data points

There are $n = 5$ data points.

Step4: Calculate the mean

Using the formula $\bar{x}=\frac{45}{5}=9$? Wait, no, wait: Wait, $5 + 7+9+11+13 = 45$? Wait, $5+7=12$, $12 + 9 = 21$, $21+11=32$, $32 + 13=45$. Then $\bar{x}=\frac{45}{5}=9$? Wait, but wait, let me check again. Wait, $5+7 = 12$, $12+9=21$, $21+11=32$, $32+13=45$. Then $45\div5 = 9$. But wait, the options have a. 10, b.8, c.9, d.11. Wait, but let me recalculate the sum. $5 + 7=12$, $12+9=21$, $21+11=32$, $32+13=45$. Yes, sum is 45, number of terms is 5. So mean is $45/5 = 9$. Wait, but the option a is 10. Wait, did I make a mistake? Wait, no, wait: $5+7+9+11+13$. Let's add them in a different way: $(5 + 13)+(7 + 11)+9=18 + 18+9=45$. Then $45\div5 = 9$. So the mean is 9. So the correct option is c. 9. Wait, but wait, maybe I miscalculated. Wait, no, $5+7=12$, $12+9=21$, $21+11=32$, $32+13=45$. $45\div5 = 9$. So the answer is c. 9.

Wait, but wait, the original problem: the data set is 5,7,9,11,13. Let's check again. Sum: 5+7=12, 12+9=21, 21+11=32, 32+13=45. Number of elements: 5. So mean is 45/5=9. So the correct option is c. 9.

Answer:

c. 9