Data Analysis: Descriptive Statistics

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Descriptive Statistics provide simple summaries of the sample and the measures or the basic information about variables in a dataset. The Central Tendency and Variability or dispersion are the most common descriptive statistics. The measure of central tendency describes the average of the values, while the measure of dispersion concerns how spread out the values are.

Descriptive Statistics Data Analysis Tool

You can use the Data Analysis Toolpak in Excel to generate Descriptive Statistics.  For example, generate descriptive statistics for the Mathematics test scores of 15 students.

Step 1: Enter all data (Math Scores). On the Data tab, in the Analysis group, click Data Analysis. Choose Descriptive Statistics and click OK.

A dialog box appears

Step 2: Click Input Range, and highlight the scores, If you want to include the heading, check Labels in first row.

Step 3: Click Output Range, and highlight cells where you want to put the results.

Step 4: Click the Summary Statistics checkbox, if you want to put a confidence interval around the mean, click Confidence Level for Mean checkbox, then click OK.

Descriptive Statistic Results

Understanding the Descriptive Statistics Results

Mean

The mean or average is a central tendency of the data, it is the sum of the observations divided by the total number of observations.

Standard Error (Std Error)

If you calculated the standard deviation of all mean values, you would have a statistic called the standard error of the mean. The standard error of the mean is a measure of the variation of the sample mean about the population mean. The Std Error is calculated by dividing the Std Dev of the population or the sample by the square root of the total number of observations. 

Median

The median or the 50th percentile is another measure of central tendency, it is the “middle number” of the sorted data values. If the number of terms is odd, the median will be the average of the middle 2 terms.

Mode

The mode refers to the most frequent, common number in the data set.

Standard Deviation (Std Dev)

The standard deviation is a popular measure of dispersion. It measures the average distance between a single observation and the mean. A high Std Dev indicates that the data points are spread out over a wider range of values, however, a low Std Dev indicates that the data points tend to be close to the mean of the data set.

Sample Variance

The sample variance is a popular measure of dispersion. It is the simple mean of the squared distance from the mean.

Kurtosis

Kurtosis measures the heaviness of the tails in the data distribution. It is a measure of whether the data are heavy-tailed (profusion of outliers) or light-tailed (lack of outliers) relative to a normal distribution.

Skewness

Skewness measures the direction and degree of asymmetry in the data distribution. It is a test for normality in the data by dividing it by the Std Error. The skewness value can be positive, negative, or undefined.

Range

The range is the difference between the largest and smallest data values.

Minimum

Minimum is the smallest value in the data set.

Maximum

Maximum is the largest value in the data set.

Sum

The sum (or total) of the data values.

Count

Count is simply the number or count of how many items or observations you have. 

Confidence Level

The confidence level is the percentage of sample confidence intervals that you expect to capture the population mean, normally, 90%, 95%, and 99%.

Related Links:

Descriptive Statistics in Excel

Descriptive Statistics using “Data Analysis” tool in Excel

Descriptive Statistics in Excel Using the Data Analysis Tool

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