Math Problem Statement
Calculate in tabular format
Solution
It looks like you've uploaded an image asking for the calculation of the standard deviation for the data set . Let's solve this in tabular format.
Steps to calculate Standard Deviation:
- Find the mean (average) of the numbers.
- Calculate each data point's deviation from the mean.
- Square each deviation.
- Find the average of these squared deviations (this is the variance).
- Take the square root of the variance to find the standard deviation.
Data set:
Let's proceed to calculate the standard deviation using a table.
(Data) | (Deviation from Mean) | (Squared Deviation) |
---|---|---|
4 | ||
11 | ||
18 | ||
25 | ||
32 |
I'll calculate each step and fill the table now.Here is the tabular breakdown for the standard deviation calculation of the data set :
(Data) | (Deviation from Mean) | (Squared Deviation) |
---|---|---|
4 | -14 | 196 |
11 | -7 | 49 |
18 | 0 | 0 |
25 | 7 | 49 |
32 | 14 | 196 |
- Mean:
- Variance:
- Standard Deviation:
Would you like further explanation or have any questions about this?
Here are some questions to expand on:
- What is the difference between population and sample standard deviation?
- How does standard deviation differ from variance?
- In what situations is it important to use standard deviation over other measures of spread?
- Can the standard deviation ever be negative?
- How does standard deviation behave with outliers?
Tip: Always check if you're calculating for a population or a sample, as formulas differ slightly!
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Variance
Formulas
Mean: (sum of data points) / (number of data points)
Variance: (sum of squared deviations from the mean) / (number of data points)
Standard Deviation: square root of variance
Theorems
-
Suitable Grade Level
Grades 9-12
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