Question

The following data represents the US per capita total cheese consumption from the last 8 years (note: 1 just made up the data for 2023 \& 2024).
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Cheese Consumption & 40 & 40.6 & 39.5 & 41 & 42 & 42 & 43 \\
\hline Year & 2018 & 2019 & 2020 & 2021 & 2022 & 2023 & 2024 \\
\hline
\end{tabular}
Determine the mean and median for the following set of data. Work must be shown to receive credit.

Answer 1

To determine both the mean and the median of the given dataset, we will first organize the cheese consumption values and then perform the necessary calculations.

### Given Data:

- Cheese Consumption: 40, 40.6, 39.5, 41, 42, 42, 43
- Corresponding Years: 2018, 2019, 2020, 2021, 2022, 2023, 2024

### Step 1: Calculate the Mean

To calculate the mean, we follow these steps:

1. **Add all the values together**:
\[
40 + 40.6 + 39.5 + 41 + 42 + 42 + 43
\]

Let's compute the sum:
\[
40 + 40.6 = 80.6
\]
\[
80.6 + 39.5 = 120.1
\]
\[
120.1 + 41 = 161.1
\]
\[
161.1 + 42 = 203.1
\]
\[
203.1 + 42 = 245.1
\]
\[
245.1 + 43 = 288.1
\]

So, the total sum of the cheese consumption is **288.1**.

2. **Count the number of values**:
There are 7 years of data, so the count (n) is 7.

3. **Calculate the mean**:
\[
\text{Mean} = \frac{\text{Sum of values}}{n} = \frac{288.1}{7} \approx 41.1571428571
\]
Rounding this to two decimal places, the mean is approximately **41.16**.

### Step 2: Calculate the Median

To calculate the median, we must arrange the data in ascending order:

1. **Ascending order of cheese consumption**:
- 39.5
- 40
- 40.6
- 41
- 42
- 42
- 43

The ordered list is: **39.5, 40, 40.6, 41, 42, 42, 43**

2. **Determine the median**:
Since there are 7 values (an odd number), the median is the middle value. To find the middle value, we use the formula:
\[
\text{Median position} = \frac{n + 1}{2} = \frac{7 + 1}{2} = 4
\]
The 4th value in the ordered list is **41**.

### Final Results

- Mean: **41.16**
- Median: **41**

Both calculations have been shown step by step.