A printing company spends specific amounts on fixed costs every month. The costs of those fixed costs are in the table.

Monthly fixed costs
Monthly charges	Monthly cost ($)
Bank charges	414
Cleaning	2408
Computer expense	2320
Lease payments	2586
Postage	2467
Uniforms	2604


Find the sample's mean, median, range, variance, and standard deviation using technology. Round to the nearest cent, if necessary.

The mean is 
.
The median is 
.
The range is 
.
The variance is 
.
The standard deviation is 
.

Given the fixed monthly costs, let's list them out and calculate the required statistics.

**Monthly costs:**
- Bank charges: $414
- Cleaning: $2408
- Computer expense: $2320
- Lease payments: $2586
- Postage: $2467
- Uniforms: $2604

### 1. **Mean**
The mean (average) is found by summing all the values and dividing by the number of values:

\[
\text{Mean} = \frac{\sum \text{costs}}{n}
\]

where $ n = 6 $ (since there are 6 cost categories).

\[
\text{Mean} = \frac{414 + 2408 + 2320 + 2586 + 2467 + 2604}{6}
\]

Let's calculate this.

### 2. **Median**
The median is the middle value in the sorted list of numbers. If there is an even number of values, the median is the average of the two middle values.

Sorted costs: $ 414, 2320, 2408, 2467, 2586, 2604 $

Since there are 6 values, the median is the average of the 3rd and 4th values:

\[
\text{Median} = \frac{2408 + 2467}{2}
\]

### 3. **Range**
The range is the difference between the maximum and minimum values:

\[
\text{Range} = \text{Maximum} - \text{Minimum} = 2604 - 414
\]

### 4. **Variance**
The variance measures the average squared deviation from the mean. The formula for variance $ s^2 $ for a sample is:

\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]

where $ x_i $ are the individual costs and $ \bar{x} $ is the mean.

### 5. **Standard Deviation**
The standard deviation is the square root of the variance:

\[
s = \sqrt{s^2}
\]

Let's perform these calculations.Here are the calculated values:

1. **Mean**: $2133.17 (rounded to the nearest cent)
2. **Median**: $2437.50
3. **Range**: $2190
4. **Variance**: $720832.17 (rounded to the nearest cent)
5. **Standard Deviation**: $849.02 (rounded to the nearest cent)

Would you like more details or have any questions about these calculations?

Here are 5 related questions to consider:
1. How do these fixed costs impact the total monthly expenditure of the printing company?
2. What would happen to the mean and median if an additional fixed cost category were added?
3. How can understanding the variance and standard deviation help the company in financial planning?
4. Is it possible to reduce any of these fixed costs to lower the overall standard deviation?
5. How might seasonal changes affect the variance in monthly costs?

**Tip:** Understanding both the mean and standard deviation can provide insights into cost stability and help in making budgeting decisions.

A printing company spends specific amounts on fixed costs every month. The costs of those fixed costs are in the table. Find the sample's mean, median, range, variance, and standard deviation using technology. Round to the nearest cent, if necessary.

Learn how to calculate the mean, median, range, variance, and standard deviation for a set of monthly fixed costs. This problem covers core concepts in descriptive statistics, including formulas for central tendency and dispersion. Suitable for students in Grades 9-12.

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