# F.DIST Function in Excel

Part 1: Introduce

🔹 Definition: The `F.DIST` function in Microsoft Excel provides the F probability distribution.

🔹 Purpose: It’s used to determine the distribution of a data set in statistics, especially in variance analysis.

🔹 Syntax & Arguments:

syntax
```=F.DIST(x, degrees_freedom1, degrees_freedom2, cumulative) ```

🔹 Explain the Arguments in the function:

• `x`: The value at which you want to evaluate the distribution.
• `degrees_freedom1`: The numerator degrees of freedom.
• `degrees_freedom2`: The denominator degrees of freedom.
• `cumulative`: A logical value that determines the form of the function. If TRUE, `F.DIST` it returns the cumulative distribution function; if FALSE, it returns the probability density function.

🔹 Return value: The function returns the F probability distribution for the given arguments.

🔹 Remarks: Ensure that the degrees of freedom are non-negative numbers. Also, the function will return an error if `x` it is negative.

Part 2: Examples

📌 Example 1: Purpose: Determine the cumulative distribution of sales variance.

Data tables and formulas:

ABCDE
1VarianceDF1DF2F.DISTResult
20.5108`=F.DIST(A2,B2,C2,TRUE)`0.85
30.7127`=F.DIST(A3,B3,C3,TRUE)`0.90
40.3119`=F.DIST(A4,B4,C4,TRUE)`0.75

Explanation: This example evaluates the cumulative distribution of sales variance using the F.DIST function. The results indicate the probability of observing such variances in the sales data.

📌 Example 2: Purpose: Evaluate the probability density of production variance.

Data tables and formulas:

ABCDE
1VarianceDF1DF2F.DISTResult
20.4810`=F.DIST(A2,B2,C2,FALSE)`0.65
30.6911`=F.DIST(A3,B3,C3,FALSE)`0.70
40.2712`=F.DIST(A4,B4,C4,FALSE)`0.55

Explanation: This example evaluates the probability density of production variance. The results provide insights into the likelihood of observing such variances in production data.

📌 Example 3: Purpose: Determine the cumulative distribution of marketing campaign variances.

Data tables and formulas:

ABCDE
1VarianceDF1DF2F.DISTResult
20.45910`=F.DIST(A2,B2,C2,TRUE)`0.82
30.55118`=F.DIST(A3,B3,C3,TRUE)`0.87
40.35109`=F.DIST(A4,B4,C4,TRUE)`0.78

Explanation: This example evaluates the cumulative distribution of variances from different marketing campaigns. The results can help in understanding the effectiveness of each campaign.

📌 Example 4: Purpose: Evaluate the probability density of cost variances in manufacturing.

Data tables and formulas:

ABCDE
1VarianceDF1DF2F.DISTResult
20.25811`=F.DIST(A2,B2,C2,FALSE)`0.60
30.501010`=F.DIST(A3,B3,C3,FALSE)`0.68
40.30912`=F.DIST(A4,B4,C4,FALSE)`0.63

Explanation: This example evaluates the probability density of cost variances in manufacturing. Understanding these variances can help in identifying areas of cost-saving.

📌 Example 5: Purpose: Determine the cumulative distribution of customer feedback scores.

Data tables and formulas:

ABCDE
1VarianceDF1DF2F.DISTResult
20.40109`=F.DIST(A2,B2,C2,TRUE)`0.80
30.481110`=F.DIST(A3,B3,C3,TRUE)`0.84
40.38911`=F.DIST(A4,B4,C4,TRUE)`0.79

Explanation: This example evaluates the cumulative distribution of variances in customer feedback scores. Analyzing these variances can provide insights into customer satisfaction levels.

📌 Example 6: Purpose: Determine if the variance in monthly sales is significant.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Significance LevelDecisionResult
20.459100.05`=IF(F.DIST(A2,B2,C2,TRUE)<D2, "Significant", "Not Significant")`Significant
30.521180.01`=IF(F.DIST(A3,B3,C3,TRUE)<D3, "Significant", "Not Significant")`Not Significant
40.381090.10`=IF(F.DIST(A4,B4,C4,TRUE)<D4, "Significant", "Not Significant")`Significant

Explanation: This example uses the `IF` function nested with `F.DIST` to determine if the variance in monthly sales is significant based on a predefined significance level. The variance is deemed significant if the result

is less than the significance level.

📌 Example 7: Purpose: Sum the significant variances in quarterly production.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Significance LevelTotal Significant VariancesResult
20.258110.05`=SUM(IF(F.DIST(A2:A4,B2:B4,C2:C4,TRUE)<D2:D4, A2:A4, 0))`0.55
30.2010100.10
40.109120.01

Explanation: Using the `SUM` function nested with `F.DIST`, we can calculate the total of significant variances in quarterly production. Only variances that are below the significance level are summed.

📌 Example 8: Purpose: Lookup the significance level based on the variance in annual expenses.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Lookup TableSignificance LevelResult
20.301090.30 – 0.05`=VLOOKUP(A2,D2:D4,2,FALSE)`0.05
30.4011100.40 – 0.01`=VLOOKUP(A3,D2:D4,2,FALSE)`0.01
40.209110.20 – 0.10`=VLOOKUP(A4,D2:D4,2,FALSE)`0.10

Explanation: With the `VLOOKUP` function nested with `F.DIST`, we can determine the significance level for annual expenses based on a lookup table of variances.

📌 Example 9: Purpose: Calculate the average variance for those values that exceed a certain significance level in a product launch.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Significance LevelAverage VarianceResult
20.359100.05`=AVERAGEIF(D2:D4, "<"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE), A2:A4)`0.32
30.281180.01
40.331090.10

Explanation: By nesting the `AVERAGEIF` function with `F.DIST`, we can compute the average variance for those values that surpass a specified significance level. This can be useful to gauge the average variance for significant product launches.

📌 Example 10: Purpose: Determine the maximum variance still considered significant in a financial audit.

Data tables and formulas:

ABCDF
1VarianceDF1DF2Significance LevelMax Significant VarianceResult
20.408110.05`=MAXIFS(A2:A4, D2:D4, "<"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE))`0.40
30.3810100.10
40.379120.01

Explanation: Using the `MAXIFS` function nested with `F.DIST`, we can identify the highest variance that is still deemed significant based on a predefined significance level. This can be crucial in financial audits to pinpoint the most significant variances.

📌 Example 11: Purpose: Count the number of variances that are not significant in a research study.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Significance LevelCount of Non-SignificantResult
20.459100.05`=COUNTIFS(D2:D4, ">"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE))`2
30.501180.01
40.481090.10

Explanation: By nesting the `COUNTIFS` function with `F.DIST`, we can tally the number of variances that are not deemed significant. This can be beneficial in research studies to understand the number of insignificant results.

📌 Example 12: Purpose: Calculate the minimum variance still considered non-significant in a quality control test.

Data tables and formulas:

ABCDEF
1VarianceDF1DF2Significance LevelMin Non-Significant VarianceResult
20.308110.05`=MINIFS(A2:A4, D2:D4, ">"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE))`0.30
30.3210100.10
40.319120.01

Explanation: With the `MINIFS` function nested with `F.DIST`, we can determine the most minor variance that is still considered non-significant. This can be essential in quality control tests to identify the least significant conflicts.

Part 3: Tips and tricks

✨ Always ensure that the degrees of freedom are non-negative to avoid errors.
✨ Use the cumulative distribution (set `cumulative` to TRUE) to understand the overall distribution of your data.
✨ To better understand variances or anomalies in your data, use the probability density function (set `cumulative` to FALSE).
✨ Cross-check your results with graphical representations like F-distribution charts for a visual understanding.