If you have a normally distributed set of data from 200 participants, how many people would you expect to have scores within ±1 standard deviation from the mean?
This can be determined using a calculator that has statistical functions, using the normal distribution function. I don't think you would be asked to derive the actual result.
For example:
Lower Bound: 199 (these values have to be ±1 standard deviation from the mean)
Upper Bound: 201
Mean: 200
Standard Deviation: 1
The output will be 0.68. This means 68 percent of the participants are within ±1 standard deviation from the mean, so about 136 people.
It's also useful to know that this is one of the defining properties of the normal distribution. In a normal distribution, 68% of the data will be within ±1 standard deviations of the mean and 95% will be within ±2 standard deviations of the mean. You can read more here: https://www.statisticshowto.com/probability-and-statistics/normal-distributions/
Hope this helps. If you have any further questions please let me know. I can also try deriving the result if needed.
Hi @Sheyda Khan-Mohammadi,
This can be determined using a calculator that has statistical functions, using the normal distribution function. I don't think you would be asked to derive the actual result.
For example:
Lower Bound: 199 (these values have to be ±1 standard deviation from the mean)
Upper Bound: 201
Mean: 200
Standard Deviation: 1
The output will be 0.68. This means 68 percent of the participants are within ±1 standard deviation from the mean, so about 136 people.
It's also useful to know that this is one of the defining properties of the normal distribution. In a normal distribution, 68% of the data will be within ±1 standard deviations of the mean and 95% will be within ±2 standard deviations of the mean. You can read more here: https://www.statisticshowto.com/probability-and-statistics/normal-distributions/
Hope this helps. If you have any further questions please let me know. I can also try deriving the result if needed.