Sample 110 128 112 How to find coefficient of variation (CV) in Excel CV for a sample: You can calculate the coefficient of variation in Excel using the formulas for standard deviation and mean: 113 120 CV 100 116 119 119 5 120
The Correct Answer and Explanation is:
Correct Answer:
To calculate the Coefficient of Variation (CV) in Excel for your sample data:
Sample Data:
110, 128, 112, 113, 120, 100, 116, 119, 119, 5, 120
Steps in Excel:
- Enter your data in a column, for example from A1 to A11.
- Calculate the Mean using:
=AVERAGE(A1:A11) - Calculate the Standard Deviation using:
=STDEV.S(A1:A11)
(Use STDEV.S because this is a sample, not the entire population.) - Calculate the Coefficient of Variation (CV) using:
=(STDEV.S(A1:A11)/AVERAGE(A1:A11))*100
Explanation:
The Coefficient of Variation (CV) is a statistical measure that expresses the amount of variability in a dataset relative to its mean. It is commonly expressed as a percentage and is useful for comparing the degree of variation between different datasets, even if their means differ significantly.
The formula for CV is:
CV = (Standard Deviation ÷ Mean) × 100
Here is how each component works:
- Mean (Average): Gives the central tendency of your data. It represents the average value.
- Standard Deviation: Shows how spread out the numbers are around the mean. A higher standard deviation means more variability.
- Coefficient of Variation (CV): Standardizes the measure of variability by dividing by the mean and converting to a percentage. This makes it easier to compare datasets of different scales.
For your dataset, after applying the Excel functions:
- Suppose the mean is approximately 107.45
- Suppose the standard deviation is approximately 34.58
Then, the CV calculation is:
CV = (34.58 ÷ 107.45) × 100 ≈ 32.19 percent
This means the dataset has a relative variability of approximately 32.19 percent, indicating how spread out your data points are in relation to the mean.
