1152 LearnersLast updated on June 18th, 2025
Descriptive Statistics
Descriptive statistics is the branch of statistics that uses the method of summarizing and organizing data to reveal patterns and trends. The techniques that are used will help us present the descriptive data clearly by using tables, graphs, and charts, without making any predictions or inferences. We shall now learn more about descriptive statistics in the topic.
What is Descriptive Statistics?
Descriptive statistics is a branch of statistics that is used and also focuses on summarizing and organizing data to make it easily interpretable. It involves different measures that each describes the data like measures of central tendency, measures of dispersion and measures of frequency distribution. Some key takeaways are:
- Descriptive statistics summarizes or describes the characteristics of a dataset.
- Descriptive statistics consists of three basic categories of measurements: measures of variability, measures of central tendency and measures of frequency distributions.
- Measures of central tendency include mean, median, and mode.
- Measures of variability include range, variance, standard deviation.
- Measures of frequency distribution include the occurrence of data, frequency counts, class intervals.
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What are the Types of Descriptive Statistics
There are many types of descriptive statistics. Descriptive statistics can be categorized into three types:
- Measures of Central Tendency
- Measures of Variability
- Measures of Frequency Distribution
Let us now understand the types of descriptive statistics:
Measures of Central Tendency:
We use the measures of central tendency to describe the center or average of a data set. The types of measures that are used to measure the central tendency is:
Mean: Mean is the average of all the values in the data set. We calculate the mean by adding up all the values and dividing the result by the number of observations
Median: Median is the middle value of an ordered data set. We calculate the median by finding the middle value of the dataset if the dataset is odd. If the dataset is even, then we average the middle values to get the median.
Mode: Mode is the most frequently occurring number in a dataset.
Measures of Variability:
We use different measures of variability to show how the data is spread or distributed. To check the spread or distribution of data, we use the following measures:
Range: Range is the difference between the highest and lowest points in a given distribution.
Variance: Variance measures how the data points differ from the mean.
Standard Deviation: Standard deviation measures the dispersion or spread of data points around the mean in the dataset.
Interquartile Range (IQR): IQR is the difference between the third quartile and the first quartile, showing the spread of the middle 50% of data.
Measures of Frequency Distribution:
The use of Frequency Distribution Table is a useful tool to summarize the data and show how data points are distributed across different categories. The frequency table includes measures like:
Data Intervals: Data intervals or also known as classes or categories are based on the range. This is useful for large datasets or continuous data.
Frequency Counts: The frequency counts or “f” is the number of times a data value appears in a dataset. It helps us in understanding how common or rare certain values are.
Relative Frequency: The relative frequency is a proportion of the occurrences of a particular class relative to the total number of observations.
Cumulative Frequency: It is the running total of frequencies up to a certain class interval.
Difference between Descriptive Statistics vs Inferential Statistics
There are a lot of differences between descriptive and inferential statistics. Let us now see the differences of descriptive statistics and inferential statistics in the given table mentioned below:
| Descriptive Statistics | Inferential Statistics |
| Descriptive statistics summarizes and organizes the data |
Inferential statistics draws conclusions and makes predictions from data |
| Descriptive statistics uses complete data from a sample or population | It uses sample data to estimate population parameters. |
| It uses measures of tendency (mean, median, mode), dispersion (range, variance, standard deviation), and frequency distributions. | It uses hypothesis testing, confidence intervals, regression analysis, correlation, and probability distributions. |
| We use graphs to visually represent the data | Statistical tests and models are used to visually represent the data |
| It is 100% accurate for the given data | It contains some uncertainty due to sampling errors |
How to represent Descriptive Statistics
There are various ways to represent descriptive statistics. Some of the ways are mentioned below:
Numerical Representation:
We use this method as it provides key measures to summarize data like mean, median, and mode. It also uses measures of dispersion like range, variance, and standard deviation. Descriptive data uses measures of position like percentiles and quartiles and z-scores.
Tabular Representation:
This type of representation is used to organize and summarize data for easy interpretation. We use the frequency distribution table, the grouped frequency table and the cumulative frequency table to represent the organized form of data.
Graphical Representation:
We use this type of representation to visualize the data and help us in finding patterns and trends. Some types of graphs used are bar charts, histograms, pie charts, box plots, scatter plots and line graphs.
Common mistakes and How to Avoid Them in Descriptive Statistics
Students tend to make mistakes when they solve problems related to descriptive statistics. Let us now see the common mistakes they make and the solutions to avoid them:
Mistake 1
Confusing Descriptive and Inferential Statistics
Students sometimes make the mistake of confusing descriptive and inferential statistics. They sometimes use descriptive statistics to make predictions. Students should remember that descriptive statistics only summarizes and organizes the data. They cannot be used to make predictions and generalize the population.
Mistake 2
Misinterpreting Measures of Central Tendency
Students at times assume that mean always represents the typical value. They should remember to check for skewness or outliers; use the median for skewed data.
Mistake 3
Ignoring the Outliers
Students sometimes do not consider the impact of extreme value. They should practice the use of box plots or z-scores to detect outliers and determine whether to keep them or remove them.
Mistake 4
Misusing the Range as a Measure of Spread
Students should not solely rely on the range, as the range is sensitive to outliers. Students should instead use interquartile range (IQR) or standard deviation for better measure of dispersion.
Mistake 5
Using the Wrong Measure of Spread
Students sometimes apply standard deviation to a skewed dataset without considering the alternatives. Students should use IQR instead of standard deviation for skewed data.
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Solved examples on Descriptive Statistics
Problem 1
Compute the mean of the data set: 5, 10, 15, 20, 25.
The mean is 15.
Explanation
Sum the values:
5 + 10 + 15 + 20 + 25 = 75
Count the number of observations:
5 values.
Calculate the mean:
Mean = 75/5 = 15
The mean is the arithmetic average and represents the central tendency of the dataset.
Problem 2
Find the median of the dataset: 8, 3, 12, 7, 5.
The median is 7
Explanation
Sort the data in ascending order:
[3, 5, 7, 8, 12]
Determine the middle value:
As there are 5 observations, the middle value is the 3rd value.
Median = The 3rd value is 7.
Problem 3
Determine the mode of the dataset: 2, 4, 4, 6, 7, 4, 9.
The mode is 4.
Explanation
Count the frequency of each value:
2 appears once
4 appears three times
6, 7, and 9 appear once each.
Identify the value with the highest frequency:
The number 4 appears most frequently.
Mode = 4.
Problem 4
Calculate the range of the data set: 12, 7, 9, 15, 10.
The range is 8.
Explanation
Identify the minimum and maximum values:
Minimum = 7 and Maximum = 15
Compute the range:
Range = 15 – 7 = 8.
Problem 5
Determine the quartiles and IQR for the dataset: 6, 7, 8, 10, 12, 15, 18, 20, 22.
Q1 = 7.5, Median = 12, Q3 = 19 and IQR = 11.5
Explanation
Sort the data:
[6, 7, 8, 10, 12, 15, 18, 20, 22]. (already sorted).
Find the median (Q2):
The 5th value = 12
Determine Q1 (low quartile):
Lower half: [6, 7, 8, 10] → Q1 = 7+8/2 = 7.5
Determine Q3 (upper quartile):
Upper half: [15, 18, 20, 22] → Q3 = 18+20/2 = 19
Calculate the IQR:
IQR = 19 – 7.5 = 11.5.
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FAQs on Descriptive Statistics
1.What are descriptive statistics?
2.What are the main types of descriptive statistics?
3.How do descriptive and inferential statistics differ?
4.What is mean?
5.What is mode?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
