The ages of the members of a legislature from a particular state are listed below. Find the​ mean, median, and mode of the data​ set, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why.

6060

4141

3535

4242

5353

4242

3636

5555

4444

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Part 1

Find the mean age. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The mean age is

enter your response here.

​(Round to one decimal place as​ needed.)

B.

There is no mean age.

To find the mean, median, and mode of the given ages, let's start by calculating each measure:

### 1. Mean (Average)
The mean is calculated by summing all the ages and then dividing by the number of data points.

Given ages: \(60, 41, 35, 42, 53, 42, 36, 55, 44\)

**Step 1:** Calculate the sum of the ages.

\[
60 + 41 + 35 + 42 + 53 + 42 + 36 + 55 + 44
\]

**Step 2:** Divide the sum by the total number of ages (which is 9).

\[
\text{Mean} = \frac{\text{Sum of Ages}}{\text{Number of Ages}}
\]

Let's calculate this value.The mean age is approximately \(45.3\) years (rounded to one decimal place).

### 2. Median
The median is the middle value when the data set is ordered from least to greatest.

**Step 1:** Arrange the ages in ascending order.

\[
35, 36, 41, 42, 42, 44, 53, 55, 60
\]

**Step 2:** Find the middle value. Since there are 9 data points, the median is the 5th value.

\[
\text{Median} = 42
\]

### 3. Mode
The mode is the value that appears most frequently in the data set.

In the ordered list, the number 42 appears twice, which is more frequent than any other number.

\[
\text{Mode} = 42
\]

### Summary:
- **Mean:** \(45.3\)
- **Median:** \(42\)
- **Mode:** \(42\)

Would you like to discuss these results further, or do you have any other questions?

### Related Questions:
1. How does removing an outlier affect the mean, median, and mode?
2. What happens to the mean and median if an additional age of 60 is added?
3. Can you calculate the range of this data set?
4. Why might the mean not be the best measure of center for this data set?
5. How would the mode change if another value was added?

**Tip:** Always round the mean to the nearest decimal when asked for precision, especially in practical contexts like data reporting.

The ages of the members of a legislature from a particular state are listed below. Find the mean, median, and mode of the data set, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

60, 41, 35, 42, 53, 42, 36, 55, 44

Find the mean age. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The mean age is (Round to one decimal place as needed.)
B. There is no mean age.

Learn how to calculate the mean, median, and mode of the ages of legislative members from a given data set. This problem uses core statistical concepts, including measures of central tendency. The data set includes ages like 60, 41, 35, 42, and others. Suitable for students in Grades 6-8.

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