Normal Distribution in Excel (NORMDIST)
NORMDIST or normal distribution is an inbuilt statistical function of Excel that calculates the normal distribution of a data set for which the mean and standard deviation are given.
NORMDIST function accepts four arguments–X value, mean, standard deviation, and cumulative value. The Excel 2010 replaced the NORMDIST function with NORM.DIST function.
The syntax of the normal distributionNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy. in Excel is mentioned as follows:
The arguments of the NORM.DIST function are listed as follows:
- X: This is the value for which we calculate the normal distribution.
- Mean: This is the average value of the distribution, i.e., the mean value.
- Standard Deviation: This is the standard deviationStandard DeviationStandard deviation (SD) is a popular statistical tool represented by the Greek letter 'σ' to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data's reliability. of the distribution.
- Cumulative: This is a logical value that determines the type of distribution to be used.
If the cumulative value is “true,” the function returns the cumulative normal distribution function (CDF). If the cumulative value is “false,” the function returns the normal probability density function (PDF).
Note: The NORMDIST function exists in the recent versions of Excel to support compatibility with the previous versions. However, it may not be available in future versions of Excel.
How to Use NORMDIST in Excel? (With Examples)
We have the stock price data of an organization. The stipulated stock price is 115, the overall average stock price is 90, and the standard deviation is 16.
We need to calculate the probability of the stock price at and below 115.
Let us apply the NORM.DIST in Excel.
X is the initial stock price. The mean is the overall average price. The standard deviation is given in cell B4. The distribution type used is “1,” meaning TRUE.
The result is 0.9409, which means roughly 94% of the stocks have a price below 115. In other words, the chance that the stock has a price above 115 is less than 6%.
Let us change the distribution type to the normal probability density function, i.e., FALSE (0). We get the following result.
The NORM.DIST function returns the value 0.0074, indicating that 0.74% of the stocks have their price equal to 115.
Let us consider the following data for normal distribution in Excel.
- Sample of the population (X) = 200
- Mean or average value = 198
- Standard deviation = 25
Let us apply cumulative normal distribution in Excel.
The normal distribution value is 0.53188, i.e., the probability is 53.18%.
The Characteristics of the Normal Distribution Function
- The NORM.DIST function accepts only numerical values.
- The NORMDIST function returns “#NUM! error” if the standard deviation supplied is less than or equal to zero.
- The NORMDIST function returns “#VALUE! error#VALUE! Error#VALUE! Error in Excel represents that the reference cell the user has either entered an incorrect formula or used a wrong data type (mostly numerical data). Sometimes, it is difficult to identify the kind of mistake behind this error.” if any of the supplied arguments is a non-numeric value.
- The normal PDF is a bell-shaped curveBell-shaped CurveBell Curve graph portrays a normal distribution which is a type of continuous probability. It gets its name from the shape of the graph which resembles to a bell. .
- The NORM.DIST function requires the mean and standard deviation which can be calculated by average functionAverage FunctionThe AVERAGE function in Excel gives the arithmetic mean of the supplied set of numeric values. This formula is categorized as a Statistical Function. The average formula is =AVERAGE( and STDEV.S functionSTDEV.S FunctionThe standard deviation shows the variability of the data values from the mean (average). In Excel, the STDEV and STDEV.S calculate sample standard deviation while STDEVP and STDEV.P calculate population standard deviation. STDEV is available in Excel 2007 and the previous versions. However, STDEV.P and STDEV.S are only available in Excel 2010 and subsequent versions. respectively.
Frequently Asked Questions
The NORM.DIST function calculates the PDF and the CDF of a data set. The function returns the probability that the variable X falls below or at a given value.
The NORM.DIST function is used in stock markets to quantify risk and return. It helps strike a balance between the risk and return of an investment. This function is also used in hypothesis testing.
The output of a normal distribution is a bell-shaped curve defined by its input value, X. The CDF returns the probability of a number below a given value. The PDF returns the probability of a number at a point in the data set.
If the cumulative value is “true,” the NORM.DIST function returns a value that is equal to the area on the left side of the input. However, if the cumulative value is “false,” the function returns a value that corresponds with the input value on the curve.
The NORM.S.DIST function calculates the standard normal distribution for a specific value. The mean of a standard normal distribution is zero and the standard deviation is one.
The formula of NORM.S.DIST function is stated as follows: “=NORM.S.DIST(z,cumulative)”
“z” is the value for which we want the distribution. “Cumulative” determines the type of distribution to be returned.
- The NORMDIST function calculates the normal distribution of a data set for which the mean and standard deviation are given.
- The NORMDIST function accepts four arguments–X value, mean, standard deviation, and cumulative value.
- If the cumulative value is “true,” the NORMDIST function returns the cumulative normal distribution function (CDF).
- If the cumulative value is “false,” the NORMDIST function returns the normal probability density function (PDF).
- The normal PDF is a bell-shaped curve.
- The NORMDIST function returns two kinds of errors in ExcelErrors In ExcelErrors in excel are common and often occur at times of applying formulas. The list of nine most common excel errors are - #DIV/0, #N/A, #NAME?, #NULL!, #NUM!, #REF!, #VALUE!, #####, Circular Reference.–“#NUM!” and “#VALUE!.”
This has been a guide to the NORMDIST function in Excel. Here we discuss how to use the Normal Distribution function in Excel along with examples and downloadable templates. You may also look at these useful Excel tools –