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To calculate the mean (average) number of pushes, we need to use the data displayed in the histogram. Here's the step-by-step process:

1. **Identify the number of pushes (x)** and their corresponding frequency (f):
   - Pushes = 4, Frequency = 9
   - Pushes = 5, Frequency = 2
   - Pushes = 6, Frequency = 3
   - Pushes = 7, Frequency = 2
   - Pushes = 8, Frequency = 2
   - Pushes = 9, Frequency = 1
   - Pushes = 12, Frequency = 1

2. **Multiply each number of pushes by its frequency** to get the total number of pushes for each category:
   - \( 4 \times 9 = 36 \)
   - \( 5 \times 2 = 10 \)
   - \( 6 \times 3 = 18 \)
   - \( 7 \times 2 = 14 \)
   - \( 8 \times 2 = 16 \)
   - \( 9 \times 1 = 9 \)
   - \( 12 \times 1 = 12 \)

3. **Add up all the products** (total pushes):
   \[
   36 + 10 + 18 + 14 + 16 + 9 + 12 = 115
   \]

4. **Add up the total number of rats** (total frequency):
   \[
   9 + 2 + 3 + 2 + 2 + 1 + 1 = 20
   \]

5. **Calculate the mean**:
   \[
   \text{Mean} = \frac{\text{Total Pushes}}{\text{Total Rats}} = \frac{115}{20} = 5.75
   \]

Thus, the mean number of pushes on the 11th day is **5.75**.

Do you have any questions or need further details? Here are some related questions:

1. How does changing the frequency distribution affect the mean?
2. What would be the median number of pushes for this data?
3. How do outliers, like the rat with 12 pushes, affect the mean?
4. How would you calculate the mode of this data set?
5. Could the standard deviation be calculated, and what would it tell us?

**Tip**: The mean is sensitive to extreme values, so always check for outliers!

Twenty lab rats are taught to push a lever in their cage to drop a food pellet. The number of pushes by each rat is recorded on the 11th day and displayed in a histogram. Calculate the mean number of pushes on the 11th day. Do not round.

Learn how to calculate the mean number of lever pushes by 20 lab rats based on a frequency histogram. This problem covers key statistical concepts such as mean and frequency distribution. Suitable for students in Grades 6-8.

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