Data Handling
Mean, median, mode, and range from grouped data
Data Handling: Measures from Grouped Data
When data is presented in groups (e.g. 10–19, 20–29), we estimate the mean using midpoints, identify the modal class (group with highest frequency), and find the interval containing the median.
Example
Calculating from a Frequency Table
Marks | Frequency | Midpoint | f × midpoint
10–19 | 3 | 14.5 | 43.5
20–29 | 7 | 24.5 | 171.5
30–39 | 5 | 34.5 | 172.5
Total | 15 | | 387.5
Estimated mean = 387.5 ÷ 15 = 25.8
Modal class = 20–29 (highest frequency)
Range
Range = highest value − lowest value. It tells us how spread out the data is. A large range means data is widely spread; a small range means data is clustered close together.
Note
Remember
For grouped data: mean is estimated using midpoints, mode becomes modal class, and median is in the group where the cumulative frequency passes the middle position.
Key Vocabulary
FrequencyHow many times a value or group appears in data
Grouped dataData organised into intervals or classes
Modal classThe group with the highest frequency
RangeThe difference between the highest and lowest values
MidpointThe middle value of a class interval
SASL Avatar
Loading avatar...
1 / 5
Frequency
Speed: