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

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Question: 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)

Options:

  1. 8
  2. 16
  3. 32
  4. 64

Correct Answer: 32

Exam Year: 2023

Solution: 

In a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean. SD = √16 = 4. Range = 20 ± 2*4 = 20 ± 8 = 12 to 28.

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

Practice Questions

Q1
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)
  1. 8
  2. 16
  3. 32
  4. 64

Questions & Step-by-Step Solutions

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.
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