The following data give the total food expenditures (in dollars)
for the past one month for a sample of 20 families.

1125 530 1234 595 427 872 1480 699 1274 1187
933 1127 716 1065 934 930 1046 1199 1353 441

a. Calculate the mean and median for these data.
b. Calculate the 20% trimmed mean for these data.

Let's tackle the problem step by step:

### a. Calculate the Mean and Median

1. **Mean** is the sum of all the data values divided by the number of data points.
   \[
   \text{Mean} = \frac{\sum \text{(all data points)}}{n}
   \]
   where $ n $ is the number of data points.

2. **Median** is the middle value when the data is ordered. If there is an even number of data points, the median is the average of the two middle values.

### b. Calculate the 20% Trimmed Mean

A **trimmed mean** is calculated by removing a percentage of the lowest and highest data values before calculating the mean. For a **20% trimmed mean**:

- Remove the lowest 10% and highest 10% of the data points.
- For 20 data points, remove 10% from each end, which is 2 values from the lowest and 2 from the highest.
- Calculate the mean of the remaining 16 values.

I'll now calculate the mean, median, and 20% trimmed mean for these values.Here are the results:

### a. Mean and Median:
- **Mean**: \$958.35
- **Median**: \$990.00

### b. 20% Trimmed Mean:
- **20% Trimmed Mean**: \$966.63

Would you like further details on any of the steps, or have any other questions?

Here are five related questions you might find helpful:
1. How does trimming affect the mean in skewed data?
2. What is the impact of outliers on the mean vs. the median?
3. How can we compute the mode of this dataset?
4. What is the variance and standard deviation of these expenditures?
5. How does a 10% trimmed mean differ from a 20% trimmed mean?

**Tip**: Trimming data helps reduce the influence of outliers, making the mean more representative of the central tendency.

The following data give the total food expenditures (in dollars) for the past one month for a sample of 20 families.

1125 530 1234 595 427 872 1480 699 1274 1187
933 1127 716 1065 934 930 1046 1199 1353 441

a. Calculate the mean and median for these data.
b. Calculate the 20% trimmed mean for these data.

Learn how to calculate the mean, median, and 20% trimmed mean for a dataset of total food expenditures from 20 families. This problem introduces statistical concepts like central tendency and trimmed mean, making it perfect for high school students in Grades 10-12.

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