Grouped Data — Step-Deviation Method & Ogive explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Grouped data is data arranged in class intervals, such as , , and .
Grouping makes large data sets easier to read and calculate with.
In this lesson, you learn how to find averages from grouped data and how to understand an ogive.
Grouped data is used when there are many values. Instead of writing every value separately, we group values into intervals.
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A class interval is one group, such as . Frequency tells how many observations are in that interval.
The class mark is the middle value of a class interval. It represents that whole interval during calculation.
Cumulative frequency means running total. It shows how many observations are less than or equal to a class boundary.
An ogive is a cumulative frequency graph. It helps us estimate the median and understand how data builds up.
Meaning: Class intervals are groups used to organise data.
Definition: A class interval is a range of values, such as .
If marks are grouped as , , and , each range is a class interval.
Meaning: Class mark is the middle value of a class interval.
Definition: Class mar.
For , class mar.
Meaning: Grouped mean estimates the average using class marks.
Definition: Grouped mean is the mean found from frequencies and class marks.
Multiply each class mark by its frequency, add the products, then divide by total frequency.
Meaning: Steeviation is a shorter method for grouped mean when intervals are equal.
Definition: Steeviation uses coded deviations from an assumed mean.
It reduces large calculations by replacing each class mark with a simpler value.
Easy
Question: Find the class mark of .
Medium
Question: Find the mean for class marks 5, 15, 25 with frequencies 2, 3, 5.
Exam-level
Question: For class marks 10, 20, 30 with frequencies 4, 6, 10, find the mean using assumed mean 20 and class width 10.
Dividing by number of classes
Why it happens: Students count rows instead of observations.
Correct approach: Divide by total frequency, not by number of intervals.
Using upper limit as class mark
Why it happens: The middle of the interval is missed.
Correct approach: Find class mark using .
Forgetting cumulative frequency is a running total
Why it happens: Each frequency is copied directly.
Correct approach: Add each new frequency to the previous total.
Using steeviation with unequal class widths
Why it happens: The method is applied from memory.
Correct approach: Check class width before using steeviation.
Why do we use class marks?
A class mark gives one representative value for the whole interval.
Is grouped mean exact?
It is an estimate because the original values inside each interval are not all known.
What does an ogive show?
It shows cumulative frequency, or how the total builds up across intervals.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.
Meaning: Cumulative frequency is a running total. An ogive graphs it.
Definition: An ogive is a cumulative frequency curve.
A leshan ogive plots upper class boundaries against cumulative frequencies.