# FAQ: What Are Descriptive Statistics? (With Examples)

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Descriptive statistics applies to many different applications. Businesses, finance professionals and data analysts rely on this form of statistics to evaluate different metrics. Additionally, if you want to observe different characteristics of a set of data, descriptive statistics give you the tools you need to organize your data. In this article, we answer several descriptive statistics FAQs, including what it is, who uses it and what types of measurements you can take with descriptive statistics.

## What are descriptive statistics?

Descriptive statistics use the measures of central tendency to summarize an entire population or a sample data set. This type of statistics also provides insight into the variability or spread of the values by taking these measures from a data set. Using these measurements, descriptive statistics focus on assigning characteristics and specific parameters to a set of data.

Related: Definitive Guide To Understanding Descriptive Statistics

## Who uses descriptive statistics?

Many applications in fields like finance, computer science, health care and business rely on descriptive statistics. Several roles you can expect to work with these areas of mathematics include:

### Data analysts

Data analysts are the professionals who rely on descriptive statistics in their day-to-day jobs. They work with various types of data, collecting and analyzing the information to gain insight into specific topics of study. Descriptive statistics are therefore an essential method for data analysts to visualize raw data in ways that others can interpret more easily. When analyzing raw data, analysts track descriptors that summarize key details about the values that can better show the relationships between data points.

### Financial analysts

Financial analysts and investors often measure variation and central tendency to analyze profitable investment opportunities. Stockbrokers, for instance, often measure averages, variance and maximum and minimum values to determine the stocks most likely to result in returns. Wealth managers are also investment professionals who apply descriptive statistics to forecast gains for their clients.

Related: Learn About Being a Financial Analyst

### Medical researchers

In the medical field, descriptive statistics are essential for summarizing pharmaceutical studies, health care treatment outcomes and other applications involving medical research. The ability to convert raw data into meaningful interpretations enables researchers in various medical fields to support innovations and advancements in applications like diagnostics and treatments. Descriptive statistics are also necessary for analyzing and understanding the outcomes potential medical applications can have on patients.

### Engineers

Engineers across many specialties often use descriptive statistics to establish parameters for different projects. In civil engineering, for example, an engineer may rely on descriptive statistics to design the most viable structure for their client. Software engineers also apply descriptive statistics to design and implement algorithms in software applications. Engineers in the sciences, like biochemical engineers, may also use descriptive statistics to test designs involving chemical and biological processes.

### Computer programmers

Computer programmers in machine learning use descriptive statistics to evaluate data that a supervised machine learning system relies on to function. Programmers analyze data sets to determine the most accurate algorithms for achieving the desired outcomes they input into a system. Because descriptive statistics summarize data for interpretation, programmers are able to determine viable approaches to organizing and managing coding data in a machine learning environment.

### Business analysts

Business analysts use descriptive statistics to analyze various processes within their organizations. Sales, marketing and budgeting all require statistical information to make important decisions. For instance, descriptive analytics in marketing can provide insight into average customer spend, purchasing trends and successful product variations. Using descriptive statistics in these ways is beneficial for businesses to gain insight into methods for increasing revenue and profitability.

Related: A Guide to Statistics for Business

## What are the differences between inferential and descriptive statistics?

Descriptive statistics only focus on converting raw data into measurements that provide information about the properties of a given sample of data. Typically, you take a smaller sample from a larger population and group these data according to the different descriptive measures. This process of analyzing and visualizing data on a graph doesn't take into account any generalizations or draw any conclusions from the data. In contrast, inferential statistics seeks to draw conclusions and make inferences about a population based on a random sampling of the population.

Because you're essentially testing a hypothesis with inferences about a sample set of data, inferential statistics also require specific measurements to ensure accuracy. The rate of error measures the probability of the hypothesis being incorrect, and the confidence interval represents the range of values the population is likely to fall between. Inferential statistics also use regression analysis to test the relationships between dependent and independent variables in order to calculate correlative and causative relationships.

Related: Descriptive vs. Inferential Statistics: What's the Difference?

## What are the measurement types in descriptive statistics?

Within statistical approaches are measures you can take to find out more about a set of data. There are four main types of measures in descriptive statistics:

### 1. Central tendency

Central tendency is essential to descriptive statistics because it encompasses important information about a data set. An important metric within this measurement type is the mean or the average. While understanding how data points collect in a median and repeat in modes is important, applying mean to a sample set is especially useful for central tendency. Data analysts wanting to understand the most common response on a survey would measure the average of the data set. Median and mode can then show the analysts the locations on a graph where values gather the most and which values tend to repeat.

### 2. Position

Position measurements give locations to data points in a set in relation to one another. Position measurements in descriptive statistics rank data values according to quartile and percentile rankings. Using position in descriptive statistics becomes necessary when comparing data values to a standardized metric, such as test scores.

### 3. Frequency

Frequency represents the rate at which a specific data value occurs in a data set. This type of measurement is useful in applications recording binary outcomes, such as a survey with "yes" and "no" responses. Frequency also counts the values that occur within a given data set. Calculating percentages, rates or ratios from a data set in descriptive statistics often requires frequency measurements.

### 4. Variation

Variation in descriptive statistics measures the spread of points within a data set. This spread can tell you about the range, which is the difference between the maximum and minimum points of the data. Variation measures also include the standard deviation, which shows you the difference between the observed data and the data's mean. Variation measures are important when measuring how spread apart the data points are within a set. If the values are so spread out that it affects the mean, variance in descriptive statistics shows where this effect occurs in the data.

Related: What Is Variance?

## What are some examples of descriptive statistics?

For additional insight into working with the four measurement types in descriptive statistics, the examples below show how to apply each measure for the example data set of exam scores {66.3, 65, 66.7, 63, 72, 89.4, 77.1, 72, 34, 72, 79.2, 83}:

### Measures of central tendency example

Measuring central tendency requires ordering the values in the data set from least to greatest. Using the exam scores {66.3, 65, 66.7, 63, 72, 89.4, 77.1, 72, 34, 72, 79.2, 83}, ordering the values results in {34, 63, 65, 66.3, 66.7, 72, 72, 72, 77.1, 79.2, 83, 89.4}. Once the values are in numerical order, you can take each measure of central tendency as:

Mean: Add all the values together and divide by the number of values in the set. Using the exam scores, this results in (34 + 63 + 65 + 66.3 + 66.7 + 72 + 72 + 72 + 77.1 + 79.2 + 83 + 89.4) ÷ 12 = 839.7 ÷ 12 = 69.975 = 70.

Median: The median is the value that occurs in the center of the data set. Because there are 12 exam scores, the median becomes the average of the two values in the center, resulting in (72 + 72) ÷ 2 = 72.

Mode: Mode represents the value in the set that occurs the most. In the example exam scores, 72 is the mode.

### Measuring position example

Using descriptive statistics, you can determine the positions of the exam scores when plotting these values on a graph. Finding the percentile rank requires knowing the percentile of a value, and the quartile rank uses the interquartile range to give positions to the exam scores within each quarter of the set. Finding the percentile and quartile ranks, in this case, would result in:

Percentile rank: The percentile rank shows the percentage of scores falling at or below a certain score. Because there are 12 exam scores, the percentile rank of a score of 65 would be within the 25th percentile, and a score of 79.2 would be within the 75th percentile.

Quartile rank: Finding the interquartile range results in 12.5, which describes the difference between the scores at the 75th and 25th quartiles. When applying statistical formulas for quartile rank, this shows the first quartile ending at 65.65, the second quartile ending at 72, the third quartile ending at 78.15 and the fourth quartile at 89.4.

Related: How To Calculate Percentile Rank (With Example)

### Measuring frequency example

Measuring the frequency of a value within a data set involves calculating the percentage of times a specific value occurs. Using the mode of the exam scores, you can calculate the rate at which a score of 72 occurs out of every 12 exam scores. Because a score of 72 occurs three out of 12 times, frequency measures this as (3 repeated scores) ÷ (12 scores) = 0.25, or a 25% frequency rate of 72 appearing as an exam score.

### Measures of variation example

Variance and spread are necessary for understanding how far apart the exam scores are from one another. Using the formulas for calculating range and standard deviation, you can apply variance to the exam scores {34, 63, 65, 66.3, 66.7, 72, 72, 72, 77.1, 79.2, 83, 89.4} as:

Range: Find the minimum and maximum values and subtract for the difference. The maximum score in the set is 89.4, and the lowest is 34, resulting in a range of (89.4 - 34) = 55.4.

Standard deviation: The standard deviation tells you about the average interval spread between values. To find the standard deviation of the exam scores, calculate the squared differences of each value and find the mean of these values, which results in (1,296 + 49 + 25 + 13.69 + 10.89 + 4 + 4 + 4 + 50.41 + 84.64 + 169 + 376.36) ÷ 12 = (2,086) ÷ 12 = 173.

Maximum and minimum: The highest score in the set is the maximum and the lowest score in the set is the minimum. Therefore, the maximum for the example data set is 89.4 and the minimum is 34.

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