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The image shows a table containing the number of school dinners 25 students had in one week, along with a frequency count of each number. The table is followed by two questions:

### Table:
| **Number of school dinners** | **Frequency** |
|------------------------------|---------------|
| 0                            | 1             |
| 1                            | 3             |
| 2                            | 0             |
| 3                            | 4             |
| 4                            | 2             |
| 5                            | 15            |

### Questions:
1. **What is the median number of school dinners?**
   - Options: a) 2, b) 3, c) 4, d) 5

2. **What is the mean number of school dinners?**
   - Options: a) 1, b) 2, c) 3, d) 4, e) 5

---

### **Solution for Median:**

To find the median, we need to list all the data points in ascending order. Here’s the list based on the frequency table:

- 0 appears 1 time
- 1 appears 3 times
- 2 appears 0 times (so it doesn't appear)
- 3 appears 4 times
- 4 appears 2 times
- 5 appears 15 times

This gives us the ordered list of dinners:
\[ 0, 1, 1, 1, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 \]

Since there are 25 students (an odd number), the median is the middle value, which is the 13th value.

Looking at the ordered list:
- The 13th value is **5**.

So, the **median number of school dinners is 5**.

---

### **Solution for Mean:**

The mean is calculated by dividing the total number of dinners by the total number of students.

- Sum of all dinners:
  \[
  (0 \times 1) + (1 \times 3) + (2 \times 0) + (3 \times 4) + (4 \times 2) + (5 \times 15) = 0 + 3 + 0 + 12 + 8 + 75 = 98
  \]

- Total number of students = 25

- Mean = \(\frac{98}{25} = 3.92\)

The closest value is approximately **4**.

So, the **mean number of school dinners is 4**.

---

Would you like further details or explanations on these calculations? Here are 5 related questions:

1. How is the median affected if the number of students increases?
2. What is the mode of the school dinners from this data?
3. How would the mean change if two more students had 5 dinners each?
4. How would you calculate the range of this data set?
5. Can you explain why the median and mean are different in this case?

**Tip:** When calculating the median for an odd set of numbers, always find the middle position directly; for an even set, take the average of the two middle values.

Amy did a survey of the number of school dinners 25 students had in one week. The frequency table shows this information. What is the median and mean number of school dinners?

This problem involves finding the median and mean number of school dinners based on a frequency distribution for 25 students. Concepts such as frequency distribution, data ordering, and the calculation of mean and median are covered.

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