What Are Descriptive Statistics? 4 Measurements and Examples

Statistics is a science that involves collecting, organizing, and interpreting large amounts of numerical data. Among the types of statistics, descriptive statistics is the most useful when you want to analyze and describe an entire dataset, and understanding the components of descriptive statistics can help you perform these calculations.

Let’s discuss everything you need to know about descriptive statistics, including its definition, users, calculations involved, and real-life examples.

1. WHAT IS DESCRIPTIVE STATISTICS?

Descriptive statistics refers to a method of summarizing and meaningfully describing an entire dataset or population.

Professionals use descriptive statistics solely to present data in a way that makes it easier to read and identify patterns. When summarizing data, experts often use several types of descriptive statistics simultaneously to provide a complete picture of the dataset they are analyzing.

Descriptive statistics are important because they offer a way to present large datasets in an easily understandable manner.

2. WHO USES DESCRIPTIVE STATISTICS?

Many applications in fields such as finance, computer science, healthcare, and business rely on descriptive statistics. Some roles you can expect to work with these mathematical areas include:

Data Analysts

Data analysts are professionals who rely on descriptive statistics in their daily work. They work with various types of data, collecting and analyzing information to better understand specific research topics.

As a result, descriptive statistics is an essential method for data analysts to visualize raw data in ways that others can more easily interpret. When analyzing raw data, analysts track summary descriptions of key details that can better highlight relationships between data points.

Financial Analysts

Financial analysts and investors often measure variation and central tendencies to analyze profitable investment opportunities.

For example, stockbrokers often measure the mean, variance, and maximum and minimum values to identify stocks that are most likely to yield profits. Asset managers are also investment professionals who apply descriptive statistics to forecast returns for their clients.

Medical Researchers

In the healthcare field, descriptive statistics are essential for summarizing pharmaceutical studies, healthcare treatment outcomes, and other applications related to medical research.

The ability to convert raw data into meaningful interpretations allows researchers in various medical fields to support innovations and advancements in applications such as diagnosis and treatment. Descriptive statistics are also necessary for analyzing and understanding the outcomes that potential medical applications may bring to patients.

Engineers

Engineers across various disciplines often use descriptive statistics to establish parameters for different projects.

For example, in civil engineering, an engineer might rely on descriptive statistics to design the most feasible structure for their client.

Software engineers also apply descriptive statistics to design and implement algorithms in software applications.

Engineers in scientific fields, such as biochemical engineers, may also use descriptive statistics to test designs related to chemical and biological processes.

Computer Programmers

Computer programmers in machine learning use descriptive statistics to evaluate the data on which supervised learning systems rely to function.

Programmers analyze datasets to identify the most accurate algorithms for achieving the desired outcomes they program into the system. Since descriptive statistics summarize data for interpretation, programmers can determine effective methods for organizing and managing encoded data within machine learning environments.

Business Analysts

Business analysts use descriptive statistics to evaluate various processes within their organizations. Sales, marketing, and budgeting all require statistical insights to make key decisions.

For example, descriptive analysis in marketing can provide insights into average customer spending, purchasing trends, and successful product variations. Using descriptive statistics in these ways benefits businesses by offering a clearer understanding of methods to increase revenue and profitability.

3. WHAT ARE THE MEASURES IN DESCRIPTIVE STATISTICS?

Within statistical methods are the measures you can perform to learn more about a dataset. There are four main types of measures in descriptive statistics:

Measures of Central Tendency

Central tendency is essential to descriptive statistics because it includes key information about a dataset. An important metric in this category is the mean or average value.

While understanding how data points cluster around the mean and repeat at the mode is important, applying the average value to a sample set is especially useful for identifying the central tendency.

Data analysts who want to understand the most common responses in a survey will measure the mean of the dataset. Then, the median and mode can show analysts the positions on a chart where values are most frequently collected and which values tend to repeat.

Position

Measures of position provide the location of data points in a related set. In descriptive statistics, measures of position rank data values by quartiles and percentiles.

The use of position in descriptive statistics becomes essential when comparing data values to a standardized metric, such as test scores.

Frequency

Frequency indicates how often a specific data value occurs within the dataset. This type of measurement is useful in applications recording binary outcomes, such as surveys with “yes” or “no” answers.

Frequency also counts the values occurring within a given dataset. Calculating percentages and ratios from a dataset in descriptive statistics often requires frequency measurement.

Variance

Variance in descriptive statistics measures how spread out the points in a dataset are. This difference can tell you about the range, which is the difference between the maximum and minimum data points.

Measures of variance also include standard deviation, showing you how far observed data differs from the mean value.

Measures of variance are critical when assessing how much data points vary in a set. If the values are spread out enough to impact the mean, variance in descriptive statistics will indicate where this effect occurs in the data.

4. WHAT IS AN EXAMPLE OF DESCRIPTIVE STATISTICS?

To better understand how to work with the four types of measurements in descriptive statistics, the examples below show how to apply each measure to a sample dataset of test scores:
{66.3, 65, 66.7, 63, 72, 89.4, 77.1, 72, 34, 72, 79.2, 83}

Measures of Central Tendency

Measuring central tendency requires arranging the dataset values from smallest to largest. Using the test scores {66.3, 65, 66.7, 63, 72, 89.4, 77.1, 72, 34, 72, 79.2, 83}, the ordered values are:
{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 derive each central tendency measure as follows:

• Mean: Add all the values and divide by the number of values in the set.
  Using the test scores:
  (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 appears in the middle of the dataset. Since there are 12 test scores, the median becomes the average of the two middle values, resulting in (72 + 72) ÷ 2 = 72.

• Mode: The mode represents the value that occurs most frequently in the dataset. In the test score example, 72 is the mode.

Measure position

Using descriptive statistics, you can determine the position of a test score when plotting these values on a graph. Finding the percentile rank requires knowing the percentage of a value, while the quartile rank uses the interquartile range to determine the position of a score within each quarter of the dataset.

In this case, calculating the percentile rank and quartiles results in:

• Percentile rank: The percentile rank shows the percentage of scores that fall at or below a certain score. Since there are 12 test scores, the percentile rank of a score of 65 would fall in the 25th percentile, and the score of 79.2 would fall in the 75th percentile.
• Quartile rank: Finding the interquartile range yields a result of 12.5, describing the difference between scores at the 75th and 25th quartiles. By applying statistical formulas for quartile ranks, we find that the first quartile ends at 65.65, the second quartile ends at 72, the third quartile ends at 78.15, and the fourth quartile is 89.4.

Frequency measurement

Measuring the frequency of a value in the dataset involves calculating the percentage of times a specific value occurs. Using the mode of the test scores, you can determine the rate at which a score of 72 appears among the 12 test scores.

Since 72 appears three out of 12 times, the frequency is measured as (3 repeated scores) ÷ (12 scores) = 0.25, or a 25% frequency rate for 72 appearing as a test score.

Measure variance

Variance and deviation are essential to understand how far apart the test scores are. By using formulas for range and standard deviation, you can apply variance to the test scores {34, 63, 65, 66.3, 66.7, 72, 72, 72, 77.1, 79.2, 83, 89.4} as follows:

• Range: Find the minimum and maximum values and subtract to get the range. The highest score in the set is 89.4 and the lowest is 34, resulting in a range of (89.4 – 34) = 55.4.
• Standard deviation: Standard deviation tells you about the average distance between values. To find the standard deviation of the test scores, square the deviations of each value and calculate their average. The result is (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 dataset is the maximum, and the lowest score is the minimum. Therefore, the maximum for this sample dataset is 89.4, and the minimum is 34.

5. SUMMARY

The article above has summarized the basic information about the topic of descriptive statistics, its target users, the types of measurements used, and examples.

Descriptive statistics apply to various applications. Businesses, financial professionals, and data analysts rely on this form of statistics to evaluate industry-specific metrics.

In addition, if you want to observe different characteristics of a dataset, descriptive statistics provide you with the necessary tools to organize your data effectively.