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The problem asks for three statistical measures—mode, median, and mean—based on the given frequency distribution for the number of animals in a litter.

The data is structured as follows:

| Number in litter | Frequency |
|------------------|-----------|
| 1                | 2         |
| 2                | 4         |
| 3                | 7         |
| 4                | 11        |
| 5                | 8         |
| 6                | 4         |
| 7                | 2         |
| 8                | 1         |

Let's solve each part:

### a) Mode (Modal value)
The mode is the value that appears most frequently. Here, the most frequent number of animals in a litter is **4**, with a frequency of 11. So, the modal value is **4**.

### b) Median (Middle value)
The median is the middle value when the data is ordered. To find the median for a grouped frequency table:

1. Calculate the cumulative frequency:
   - For 1: 2
   - For 2: 2 + 4 = 6
   - For 3: 6 + 7 = 13
   - For 4: 13 + 11 = 24
   - For 5: 24 + 8 = 32
   - For 6: 32 + 4 = 36
   - For 7: 36 + 2 = 38
   - For 8: 38 + 1 = 39

   Total frequency = 39.

2. To find the median, locate the \(n/2\) position:
   \(n/2 = 39/2 = 19.5\). The 20th value falls in the 4th group (number in litter = 4) because the cumulative frequency up to 13 is below 19.5, and the cumulative frequency up to 24 includes 19.5.

So, the **median** value is **4**.

### c) Mean (Average)
The mean is calculated as:

\[
\text{Mean} = \frac{\sum (\text{Number in litter} \times \text{Frequency})}{\text{Total frequency}}
\]

Calculating the numerator:

\[
(1 \times 2) + (2 \times 4) + (3 \times 7) + (4 \times 11) + (5 \times 8) + (6 \times 4) + (7 \times 2) + (8 \times 1)
= 2 + 8 + 21 + 44 + 40 + 24 + 14 + 8 = 161
\]

The total frequency is 39, so the mean is:

\[
\text{Mean} = \frac{161}{39} \approx 4.13
\]

So, the **mean** number in a litter is approximately **4.13**.

### Summary:
- Mode: 4
- Median: 4
- Mean: 4.13

Do you want more details on any of these? Here are five related questions to expand your understanding:

1. How do cumulative frequency distributions help in finding the median?
2. Why is the mode important in understanding the most frequent occurrences in a dataset?
3. What does the mean tell us compared to the median and mode?
4. How would the mean change if there were outliers in the data?
5. Can the mode be different from the median and mean in all datasets?

**Tip:** When analyzing grouped data, always calculate cumulative frequencies to easily find the median!

Calculate the mode, median, and mean based on the given frequency distribution for the number of animals in a litter.

This problem involves calculating the mode, median, and mean from a frequency distribution of litter sizes. Learn how to find these descriptive statistics, including calculating the cumulative frequency for the median and using summation for the mean.

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