Question

Question 1 A) Use the data set below to answer the true/false questions in the table. {3, 7, 8, 8, 12, 15, 15, 20, 21, 24} (4 points) True False The mean of the data set is 13.3. The median of the data set is 15. The mode of the data set is 8 and 15. The range of the data set is 21.

Answer 1

Let's analyze the data set: {3, 7, 8, 8, 12, 15, 15, 20, 21, 24}.

**1. Mean:**
To calculate the mean, we need to sum all the numbers and divide by the total count of numbers.

Sum = 3 + 7 + 8 + 8 + 12 + 15 + 15 + 20 + 21 + 24 = 3 + 7 + 8 + 8 + 12 + 15 + 15 + 20 + 21 + 24 = 138

Count of numbers = 10

Mean = Total Sum / Count = 138 / 10 = 13.8

**True/False statement**: The mean of the data set is 13.3.
**Answer**: False

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**2. Median:**
To calculate the median, we need to arrange the numbers in ascending order (already done) and find the middle value. Since there are 10 numbers (an even count), the median will be the average of the 5th and 6th numbers.

5th number = 12
6th number = 15

Median = (12 + 15) / 2 = 27 / 2 = 13.5

**True/False statement**: The median of the data set is 15.
**Answer**: False

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**3. Mode:**
The mode is the number that appears most frequently in the data set.

Looking at the data:
- 8 appears twice
- 15 appears twice
- All other numbers appear once.

So, the modes are 8 and 15.

**True/False statement**: The mode of the data set is 8 and 15.
**Answer**: True

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**4. Range:**
The range is the difference between the maximum value and the minimum value.

Max = 24
Min = 3

Range = Max - Min = 24 - 3 = 21

**True/False statement**: The range of the data set is 21.
**Answer**: True

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### Summary of True/False answers:
1. The mean of the data set is 13.3. **False**
2. The median of the data set is 15. **False**
3. The mode of the data set is 8 and 15. **True**
4. The range of the data set is 21. **True**