In a normal distribution, approximately what percentage of data items fall within one standard deviation of the mean(in both directions)?
To determine the percentage of data items that fall within one standard deviation of the mean in a normal distribution, you can use the empirical rule, also known as the 68-95-99.7 rule.
According to this rule, approximately 68% of the data falls within one standard deviation of the mean. This means that if you have a normal distribution, 68% of the data will be within μ ± σ, where μ represents the mean and σ represents the standard deviation.
To calculate this, you can follow these steps:
Step 1: Determine the mean (μ) and standard deviation (σ) of your data set.
Step 2: Find the lower boundary of one standard deviation below the mean (μ - σ).
Step 3: Find the upper boundary of one standard deviation above the mean (μ + σ).
Step 4: Calculate the percentage of data falling within this range.
Based on the empirical rule, approximately 68% of the data will fall within this range (μ ± σ).
For example, if the mean is 50 and the standard deviation is 10, the range within one standard deviation would be from 40 to 60. Therefore, approximately 68% of the data items would fall within this range.