If the variance of a data set is 16, what is the range of the data if the minimu

₹0.0

Question: If the variance of a data set is 16, what is the range of the data if the minimum value is 0? (2023)

Options:

Correct Answer: 8

Exam Year: 2023

Solution:

Standard deviation = √16 = 4. If the minimum is 0, the maximum can be 4, thus range = 4 - 0 = 4.

If the variance of a data set is 16, what is the range of the data if the minimum value is 0? (2023)

If the variance of a data set is 16, what is the range of the data if the minimum value is 0? (2023)

Step 1: Understand that variance is a measure of how spread out the numbers in a data set are. The variance given is 16.
Step 2: Calculate the standard deviation by taking the square root of the variance. So, √16 = 4.
Step 3: Recognize that the standard deviation tells us how far the data points typically are from the mean (average).
Step 4: Since the minimum value of the data set is 0, and the standard deviation is 4, the maximum value can be found by adding the standard deviation to the minimum value. Thus, maximum = 0 + 4 = 4.
Step 5: Calculate the range of the data set. The range is the difference between the maximum and minimum values. So, range = maximum - minimum = 4 - 0 = 4.

Variance and Standard Deviation – Understanding the relationship between variance and standard deviation, and how they relate to the spread of data.
Range of Data – Calculating the range of a data set based on minimum and maximum values.