Given the following data, find the following:
*Round your answer to 2 decimal places as needed*



58

13

74

50

44

22

99

61

75

2

82


mean = 

median = 

midrange = 

range = 

standard deviation = 

Let's go step by step with the given data set:

### Data:
58, 13, 74, 50, 44, 22, 99, 61, 75, 2, 82

### 1. **Mean** (average):
The formula for the mean is:
\[
\text{Mean} = \frac{\text{Sum of the data}}{\text{Number of data points}}
\]

### 2. **Median** (middle value when data is sorted):
First, we need to sort the data in increasing order and find the middle value.

### 3. **Midrange** (average of the maximum and minimum values):
\[
\text{Midrange} = \frac{\text{Max value} + \text{Min value}}{2}
\]

### 4. **Range** (difference between the maximum and minimum values):
\[
\text{Range} = \text{Max value} - \text{Min value}
\]

### 5. **Standard deviation** (spread of the data):
The formula for standard deviation is:
\[
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
\]
where \( x_i \) are the data points, \( \mu \) is the mean, and \( N \) is the number of data points.

Now, let's calculate these values.Here are the calculated values for the given data set:

- **Mean** = 52.73
- **Median** = 58.00
- **Midrange** = 50.50
- **Range** = 97
- **Standard deviation** = 28.95

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the mean change if an additional data point of 100 was added?
2. How do you calculate the median if the data set has an even number of values?
3. What is the difference between standard deviation and variance?
4. How can the range help in understanding the variability of the data?
5. What effect does a very high or low outlier have on the mean and standard deviation?

**Tip:** The standard deviation provides a good measure of how spread out the data points are relative to the mean!

Given the following data, find the following:
*Round your answer to 2 decimal places as needed*

58
13
74
50
44
22
99
61
75
2
82

mean = 
median = 
midrange = 
range = 
standard deviation =

Learn how to calculate the mean, median, midrange, range, and standard deviation for the data set {58, 13, 74, 50, 44, 22, 99, 61, 75, 2, 82}. This problem involves key concepts from descriptive statistics, suitable for students in Grades 8-12.

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