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Learn how to make and use grouped frequency tables to organize and analyze data. See examples of whole numbers, decimals, and fractions with solutions and graphs.
Learn how to make a grouped frequency distribution table from a set of data. Find out how to calculate the group size, start value, lower and upper limits, and frequency for each group.
Learn how to calculate class intervals and generate grouped frequency tables for data. Enter data values and desired number of intervals, and get results with frequency, percentage, and class interval.
- The Race and The Naughty Puppy
- Grouped Frequency Table
- OH No!
- Estimating The Mean from grouped Data
- Estimating The Median from grouped Data
- Estimating The Mode from grouped Data
- Baby Carrots Example
- Age Example
- Summary
- GeneratedCaptionsTabForHeroSec
This starts with some raw data (not a grouped frequency yet) ... To find the MeanAlex adds up all the numbers, then divides by how many numbers: Mean = 59 + 65 + 61 + 62 + 53 + 55 + 60 + 70 + 64 + 56 + 58 + 58 + 62 + 62 + 68 + 65 + 56 + 59 + 68 + 61 + 6721 Mean= 61.38095... To find the MedianAlex places the numbers in value order and finds the midd...
Alex then makes a Grouped Frequency Table: So 2 runners took between 51 and 55 seconds, 7 took between 56 and 60 seconds, etc
... can we help Alex calculate the Mean, Median and Mode from just that table? The answer is ... no we can't. Not accurately anyway. But, we can make estimates.
So all we have left is: We can estimate the Mean by using the midpoints. Let's now make the table using midpoints: Our thinking is: "2 people took 53 sec, 7 people took 58 sec, 8 people took 63 sec and 4 took 68 sec". In other words we imaginethe data looks like this: 53, 53, 58, 58, 58, 58, 58, 58, 58, 63, 63, 63, 63, 63, 63, 63, 63, 68, 68, 68, 6...
Let's look at our data again: The median is the middle value, which in our case is the 11thone, which is in the 61 - 65 group: We can say "the median groupis 61 - 65" But if we want an estimated Median valuewe need to look more closely at the 61 - 65 group. At 60.5 we already have 9 runners, and by the next boundary at 65.5 we have 17 runners. By d...
Again, looking at our data: We can easily find the modal group (the group with the highest frequency), which is 61 - 65 We can say "the modal groupis 61 - 65" But the actual Mode may not even be in that group! Or there may be more than one mode. Without the raw data we don't really know. But, we can estimatethe Mode using the following formula: Est...
Example: You grew fifty baby carrots using special soil. You dig them up and measure their lengths (to the nearest mm) and group the results:
Age is a special case. When we say "Sarah is 17" she stays "17" up until her eighteenth birthday. She might be 17 years and 364 days old and still be called "17". This changes the midpoints and class boundaries. Example: The ages of the 112 people who live on a tropical island are grouped as follows: A child in the first group 0 - 9 could be almost...
For grouped data, we cannot find the exact Mean, Median and Mode, we can only give estimates.To estimate the Mean use the midpoints of the class intervals: Estimated Mean = Sum of (Midpoint × Frequency)Sum of FrequencyTo estimate the Median use: Estimated Median = L + (n/2) − BG × w where:To estimate the Mode use: Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w where:Learn how to estimate the mean, median and mode from a grouped frequency table using midpoints and cumulative frequencies. See examples with data on race times and naughty puppies.
Learn how to make and use grouped frequency tables to organise and analyse numerical data. Find definitions, examples, worksheets and related lessons on frequency tables.
Grouped Frequency Tables. This particular example is a set of data on the heights of a selection of adults. To understand what this table is saying, let’s look at the first group (also known as a class): 150<h\leq 160 150 <h ≤ 160. This notation means that all people who fall within this group are.
In a frequency table for continuous data, the group counts indicate the number of times data values fall within each group. For the height data, I used Excel and its FREQUENCY function to make the frequency table below. You can download the Excel file with the data and table: HeightFrequencyTable.
