Let's calculate the mean, median, and mode step by step.

Data Set:

$5, 8, 15, 7, 10, 22, 3, 1, 15, 10$

Step 1: Mean

The mean is the average of the numbers. We calculate it by summing all the numbers and dividing by the number of elements.

$\text{Mean} = \frac{5 + 8 + 15 + 7 + 10 + 22 + 3 + 1 + 15 + 10}{10}$ $\text{Mean} = \frac{96}{10} = 9.6$

Step 2: Median

To find the median, we need to arrange the numbers in ascending order and find the middle value(s).

Ascending order: $1, 3, 5, 7, 8, 10, 10, 15, 15, 22$

Since there are 10 values (an even number), the median is the average of the 5th and 6th values: $\text{Median} = \frac{8 + 10}{2} = \frac{18}{2} = 9$

Step 3: Mode

The mode is the number that appears most frequently.

In this data set, the number 15 and the number 10 both appear twice, so there are two modes: 10 and 15.

Summary:

• Mean: 9.6
• Median: 9
• Mode: 10, 15 (bimodal)

Now, which statements are true depends on the specific statements provided. If you'd like to provide a set of statements, I can mark the true ones for you.

Do you want more details or have any questions?

5 Related Questions:

1. How do you calculate the range of this data set?
2. What is the variance and standard deviation of this data?
3. What happens to the mean, median, and mode if you add a new data point?
4. How does the presence of multiple modes affect data analysis?
5. What is the difference between mean and median in skewed distributions?

Tip:

For symmetric distributions, the mean and median are usually very close or the same. However, in skewed distributions, they can differ significantly.