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How to Find the Standard Deviation When All You Know Is the Mean And Sample Size?

Statistics provide several different ways to classify information that is collected from a population or a particular sample from a population. Sample size, indicated by the letter "N," refers to the number of people or items that data was collected from. The mean, or average, is calculated by adding up the results for the entire sample and dividing by "N," which is the number that represents the sample size. Standard deviation, or "SD," describes the variability in the data. It compares each individual result to the mean, describing how a particular person or item compares to the average for the group.

Instructions

- 1
  Survey five people and add the total number of cars owned by the entire sample: 2 + 1 + 2 + 2 + 3 = 10. This information must be known in addition to the mean and sample size to calculate standard deviation.
- 2
  Divide the total number of cars by the mean, or average number of cars owned: 10\ 2 = 5. If the average is not known, it can be calculated by adding up the total number of cars and dividing by the number of owners: 10\5 = 2.
- 3
  Calculate "SD" by finding the square root of the result of total cars divided by the mean: the square root of 5 is 2.24, rounded to the nearest 10th place. The standard deviation, or general variability of the results, is 2.24. It can be concluded that the average number of cars owned was 2, plus or minus 2.24.

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