I have found standard deviation and the mean for a data set and have created a plot of the data now I have to find within how many standard deviation of the mean does all the data fall and I am not sure how to do this
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To determine within how many standard deviations of the mean your data falls, you need to consider the concept of the empirical rule, also known as the 68-95-99.7 rule. This rule provides a general guideline for how data tends to distribute in a normal distribution.
According to the empirical rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
To apply this rule to your data, you can follow these steps:
1. Calculate the lower and upper bounds for each range.
- Within one standard deviation: lower bound = mean - standard deviation, upper bound = mean + standard deviation.
- Within two standard deviations: lower bound = mean - (2 * standard deviation), upper bound = mean + (2 * standard deviation).
- Within three standard deviations: lower bound = mean - (3 * standard deviation), upper bound = mean + (3 * standard deviation).
2. Determine how much of your data falls within each range.
- Count the number of data points that fall between the lower and upper bounds of each range.
3. Calculate the percentage of data within each range.
- Divide the count for each range by the total number of data points and multiply by 100.
4. Interpret the results.
- Based on the percentages, you can determine how much of your data falls within each range, indicating the spread of the data around the mean.
By following these steps, you will have a clear understanding of within how many standard deviations your data falls relative to the mean.