The image shows a stem-and-leaf plot where you are asked to find the standard deviation for the group of data items.

Interpretation of the dataThe image shows a stem-and-leaf plot where you are asked to find the standard deviation for the group of data items.

Interpretation of the

• Stems represent the tens place.
• Leaves represent the units place.

Thus, the data points are:

• 28 (from stem 2 and leaf 8),
• 38, 38 (from stem 3 and leaves 3, 8),
• 48, 48 (from stem 4 and leaves 3, 8).

So, the dataset is: 28, 38, 38, 48, 48

To find the standard deviation:

1. Compute the mean (average) of the dataset.
2. Calculate the squared differences from the mean for each data point.
3. Find the average of these squared differences (variance).
4. Take the square root of the variance to get the standard deviation.

Let me calculate that for you.The standard deviation of the data set $28, 38, 38, 48, 48$ is 7.48 (rounded to two decimal places).

Would you like any further details or explanations?

Here are 5 related questions for further exploration:

1. What is the variance of this dataset, and how does it relate to standard deviation?
2. How would the standard deviation change if an additional data point was added, such as 58?
3. Can you explain the difference between standard deviation and range?
4. How is standard deviation used in data analysis to measure variability?
5. How do outliers affect the standard deviation?

Tip: When all data points in a set are the same, the standard deviation is zero because there is no variability in the data.