https://file.aiquickdraw.com/mathbot/file/1729425428613csg8k9m8.jpg

Let's solve the two parts of the problem:

### Part (a): Find the median number of goals conceded.
The table shows the number of goals conceded and their frequencies:

| Conceded Goals | Frequency |
|----------------|-----------|
| 0              | 7         |
| 1              | 9         |
| 2              | 2         |
| 3              | 4         |
| 4              | 3         |

To find the median, we need the total number of games:

\[
\text{Total number of games} = 7 + 9 + 2 + 4 + 3 = 25
\]

Since there are 25 data points, the median will be the 13th data point (since 25 is odd, the median is the middle value).

- The first 7 data points correspond to 0 goals.
- The next 9 data points correspond to 1 goal.

So, the 13th data point falls in the "1 goal" category, meaning the **median is 1**.

### Part (b): Work out the mean number of goals conceded.
To find the mean, we use the formula for the weighted mean:

\[
\text{Mean} = \frac{\sum (\text{Conceded Goals} \times \text{Frequency})}{\text{Total Frequency}}
\]

Now, calculate the sum of \((\text{Conceded Goals} \times \text{Frequency})\):

\[
(0 \times 7) + (1 \times 9) + (2 \times 2) + (3 \times 4) + (4 \times 3) = 0 + 9 + 4 + 12 + 12 = 37
\]

Now divide by the total frequency (which is 25):

\[
\text{Mean} = \frac{37}{25} = 1.48
\]

Thus, the **mean number of goals conceded is 1.48**.

---

Would you like more details or have any questions?

Here are some related questions:
1. What is the range of goals conceded in this dataset?
2. How would you calculate the mode from the given data?
3. What if the median falls between two numbers, how would you calculate it?
4. Can you explain why the mean and median are different in this dataset?
5. What is the standard deviation of the goals conceded?

**Tip:** For datasets with an odd number of entries, the median is always the middle value when data points are arranged in order.

At the end of the football season, a team analyses the number of goals they conceded each game. The table shows their information. (a) Find the median number of goals conceded. (b) Work out the mean number of goals conceded.

Analyze the number of goals conceded by a football team. Learn how to calculate the median and mean from a frequency table. In this example, the median number of goals conceded is 1, and the mean is 1.48.

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