Here is some sample data that is already in a stem-and-leaf plot:
1 | 7
2 |
3 | 6 6
4 | 2 2 6 7
5 | 0 2 4 4 6
6 | 3 6 6 8


Find the following, up to 2-3 decimal places where necessary. (If you use AOS, you may report what it gives you.) 
Hint
a. Mean 
b. Median 
c. Standard Deviation 
d. Range 
e. What is the shape of this data?
Right-Skewed
Left-Skewed
Symmetric

Let's first extract the data from the stem-and-leaf plot and organize it into a list of numbers:

- Stem 1: 17
- Stem 2: No data
- Stem 3: 36, 36
- Stem 4: 42, 42, 46, 47
- Stem 5: 50, 52, 54, 54, 56
- Stem 6: 63, 66, 66, 68

So, the list of numbers is:

\[ 17, 36, 36, 42, 42, 46, 47, 50, 52, 54, 54, 56, 63, 66, 66, 68 \]

Now, let's calculate the required statistical measures.

### a. Mean
The mean is calculated as:

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

### b. Median
To find the median, we need to arrange the data in ascending order (which is already done) and find the middle value(s). If there are an odd number of data points, the median is the middle one; if there is an even number, the median is the average of the two middle values.

### c. Standard Deviation
The standard deviation is calculated using the formula:

\[
\text{Standard Deviation} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}
\]

Where \( \mu \) is the mean, and \( N \) is the number of data points.

### d. Range
The range is calculated as:

\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]

### e. Shape of the Data
We'll infer whether the data is symmetric, right-skewed, or left-skewed based on the distribution of the numbers.

Let me calculate each value.Here are the calculated values based on the dataHere are the calculated values based on the 

### a. Mean:
\[
\text{Mean} = 49.688
\]

### b. Median:
\[
\text{Median} = 51.0
\]

### c. Standard Deviation:
\[
\text{Standard Deviation} = 13.013
\]

### d. Range:
\[
\text{Range} = 51 \quad (\text{Maximum} - \text{Minimum} = 68 - 17)
\]

### e. Shape of the Data:
Since the mean (49.688) is slightly less than the median (51.0), the data is slightly **left-skewed**.

Would you like more details on any of these, or do you have further questions?

Here are 5 related questions to explore:
1. How does skewness affect the interpretation of data distribution?
2. What is the interquartile range (IQR) for this dataset?
3. How would the shape change if outliers were present?
4. How is variance related to standard deviation?
5. How would the results change if more data points were added?

**Tip**: Skewness can influence measures like the mean and median, affecting conclusions drawn from the data.

Here is some sample data that is already in a stem-and-leaf plot:
1 | 7
2 |
3 | 6 6
4 | 2 2 6 7
5 | 0 2 4 4 6
6 | 3 6 6 8

Find the following, up to 2-3 decimal places where necessary. (If you use AOS, you may report what it gives you.) 
Hint
a. Mean 
b. Median 
c. Standard Deviation 
d. Range 
e. What is the shape of this data? Right-Skewed, Left-Skewed, Symmetric

Learn how to calculate the mean (49.688), median (51.0), standard deviation (13.013), and range (51) for a stem-and-leaf plot dataset. The problem also explains the shape of the data distribution, which is left-skewed. Suitable for students in Grades 9-12.

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