The Grand City Water and Sewer Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for water and sewer last month: 54

48

58

50

25

47

75

46

60

70

67

68

39

35

56

66

33

62

65

67 Compute the arithmetic mean. Indicate whether it is a statistic or a parameter.

To compute the arithmetic mean of the charges, we follow these steps:

1. **Sum the data values:**
   \[
   54 + 48 + 58 + 50 + 25 + 47 + 75 + 46 + 60 + 70 + 67 + 68 + 39 + 35 + 56 + 66 + 33 + 62 + 65 + 67
   \]

2. **Divide by the number of data values (n = 20):**

\[
\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}
\]

Let's compute it.

I'll sum the values first and then divide them.The arithmetic mean (average) of the charges is approximately **54.55 dollars**.

This value represents a **statistic**, because it is calculated from a sample (a subset of 20 residential customers) rather than the entire population of customers.

Would you like more details or further clarification?

Here are five related questions to expand on this concept:

1. How does the arithmetic mean change if an outlier is present?
2. What is the difference between a statistic and a parameter in more detail?
3. How would you compute the median for this dataset?
4. How do measures like variance and standard deviation relate to the mean?
5. How can we determine whether the sample size is sufficient for estimating the population mean?

**Tip:** The arithmetic mean is sensitive to extreme values (outliers), so always consider checking for these when analyzing a dataset.

The Grand City Water and Sewer Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for water and sewer last month: 54, 48, 58, 50, 25, 47, 75, 46, 60, 70, 67, 68, 39, 35, 56, 66, 33, 62, 65, 67. Compute the arithmetic mean. Indicate whether it is a statistic or a parameter.

Learn how to compute the arithmetic mean of water and sewer charges based on a sample of 20 customers. This problem involves key statistical concepts like the arithmetic mean and understanding the difference between a statistic and a parameter. Suitable for students in Grades 8-10.

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