Select the correct answer from each drop-down menu.
A comic-strip writer churns out different numbers of comic strips each day. The writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set.

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8

The data in the distribution is 
. If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is 
.

To solve this, we'll first address each part of the problem step by step.

### Part 1: Describing the Data Set

The original data set, sorted in ascending order, is:

**1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8**

This data set has 16 values. Now, let's identify the following:
- **Mean**: The mean is the average of all the numbers.
- **Median**: The median is the middle value of the data set when it is ordered. If there is an even number of values, the median is the average of the two middle values.

### Step 1: Calculating the Mean

To find the mean, add all the values together and divide by the total number of values:

\[
\text{Mean} = \frac{1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 8}{16}
\]

Summing the values:

\[
1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 8 = 56
\]

Now, divide by 16 (the total number of values):

\[
\text{Mean} = \frac{56}{16} = 3.5
\]

### Step 2: Calculating the Median

Since there are 16 numbers (an even count), the median will be the average of the 8th and 9th values. In the sorted data:

- The 8th value is 3.
- The 9th value is also 3.

Thus, the median is:

\[
\text{Median} = \frac{3 + 3}{2} = 3
\]

So, the **median** of the original data set is 3.

### Part 2: New Data Set After Two More Days

If the writer writes 5 and 7 comic strips on two more days, the new data set becomes:

**1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8, 5**

The data is now:

**1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 8**

Now, let's re-calculate the **mean** and **median** for the new data set.

### Step 3: Calculating the New Mean

Sum the values of the new data set:

\[
1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 8 = 61
\]

Now, divide by 18 (the total number of values):

\[
\text{New Mean} = \frac{61}{18} \approx 3.39
\]

### Step 4: Calculating the New Median

Since there are now 18 numbers (an even count), the median will be the average of the 9th and 10th values. In the sorted data:

- The 9th value is 3.
- The 10th value is 4.

Thus, the new median is:

\[
\text{New Median} = \frac{3 + 4}{2} = 3.5
\]

### Step 5: Finding the Difference Between the New Mean and Median

The difference between the new **mean** (3.39) and the new **median** (3.5) is:

\[
\text{Difference} = 3.5 - 3.39 = 0.11
\]

### Final Answer:

- The data in the distribution is **sorted** (as it is given in ascending order).
- The difference between the new mean and the new median is **0.11**.

Let me know if you need further details or explanations! Here are some related questions for your exploration:

1. How do you calculate the mean and median for an odd number of data points?
2. What happens to the mean and median if an extreme value (outlier) is added to the data set?
3. How does adding or removing values from a data set affect the mean and median?
4. What are the advantages of using the median over the mean for describing skewed data?
5. How can you interpret the difference between the mean and the median in real-world data?

**Tip**: The median is often a better measure of central tendency than the mean when the data contains outliers or is skewed, as it is less sensitive to extreme values.

Select the correct answer from each drop-down menu. A comic-strip writer churns out different numbers of comic strips each day. The writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8. The data in the distribution is . If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .

Learn how to calculate the mean and median for a data set of comic strips created over 16 days. Understand the impact of adding two additional values (5 and 7) to the set, and compute the difference between the new mean and median (0.11). Suitable for students in Grades 6-8.

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