A data set has a mean of 20 and a variance of 16. What is the range of the data

A data set has a mean of 20 and a variance of 16. What is the range of the data if it is normally distributed? (2023)

A data set has a mean of 20 and a variance of 16. What is the range of the data if it is normally distributed? (2023)

Step 1: Identify the mean of the data set, which is given as 20.
Step 2: Identify the variance of the data set, which is given as 16.
Step 3: Calculate the standard deviation (SD) by taking the square root of the variance: SD = √16 = 4.
Step 4: Understand that in a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean.
Step 5: Calculate the range by finding the values that are 2 standard deviations below and above the mean: 20 - 2*4 and 20 + 2*4.
Step 6: Perform the calculations: 20 - 8 = 12 and 20 + 8 = 28.
Step 7: Conclude that the range of the data is from 12 to 28.

Mean and Variance – Understanding the mean as the average value and variance as the measure of data spread.
Standard Deviation – Calculating standard deviation as the square root of variance to understand data dispersion.
Normal Distribution Properties – Applying the empirical rule that states approximately 95% of data falls within 2 standard deviations from the mean.
Range Calculation – Determining the range of data based on the mean and standard deviation in a normal distribution.