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Last updated on October 7, 2025
Descriptive statistics is the branch of statistics that uses the method of summarizing and organizing data to reveal patterns and trends. These techniques help present data clearly through tables, graphs, and charts without making predictions or inferences.We shall now learn more about descriptive statistics in the topic.
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:
There are many types of descriptive statistics. Descriptive statistics can be categorized into three types:
Let us now understand the types of descriptive statistics:
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:
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:
Measures of Frequency Distribution:
A frequency distribution table helps summarize how data points are distributed across categories. The frequency table includes measures like:
Data Intervals: Data intervals, 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.
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:
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.
Descriptive statistics help summarize and interpret large datasets in a simple way. Mastering them enables clear understanding and communication of data insights.
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:
Descriptive statistics are used to summarize and analyze data in various real-life situations. They help in identifying patterns, trends, and insights for better decision-making.
Compute the mean of the data set: 5, 10, 15, 20, 25.
The mean is 15.
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.
Find the median of the dataset: 8, 3, 12, 7, 5.
The median is 7
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.
Determine the mode of the dataset: 2, 4, 4, 6, 7, 4, 9.
The mode is 4.
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.
Calculate the range of the data set: 12, 7, 9, 15, 10.
The range is 8.
Identify the minimum and maximum values:
Minimum = 7 and Maximum = 15
Compute the range:
Range = 15 – 7 = 8.
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
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 = Q3 − Q1 = 19 − 7.5 = 11.5.
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
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!