Descriptive Statistics > Grouped Data
Contents:
What is Grouped Data?
Grouped data is data that has been bundled together in categories. Histograms and frequency tables can be used to show this type of data:
The data is grouped together by classes or bins.
Grouped Data vs. Ungrouped Data
Ungrouped data is the data you first gather from an experiment or study. The data is raw — that is, it’s not sorted into categories, classified, or otherwise grouped. An ungrouped set of data is basically a list of numbers.
Calculating the Sample Mean for Grouped Data
When you have a frequency table or other group of data, the original set of data is lost — replaced with statistics for the group. You can’t find the exact sample mean (as you don’t have the original data) but you can find an estimate. The formula for estimating the sample mean for grouped data is:
Example question: Find the sample mean for the following frequency table.
Score | Frequency ( f ) |
---|---|
Between 5 and 10 | 1 |
10 ≤ t < 15 | 4 |
15 ≤ t < 20 | 6 |
20 ≤ t < 25 | 4 |
25 ≤ t < 30 | 2 |
30 ≤ t < 35 | 3 |
TOTALS | 20 |
Step 1: Find the midpoint for each class interval. the midpoint is just the middle of each interval. For example, the middle of 10 and 15 is 12.5:
Score | Frequency ( f ) | Midpoint ( x ) |
---|---|---|
Between 5 and 10 | 1 | 7.5 |
10 ≤ t < 15 | 4 | 12.5 |
15 ≤ t < 20 | 6 | 17.5 |
20 ≤ t < 25 | 4 | 22.5 |
25 ≤ t < 30 | 2 | 27.5 |
30 ≤ t < 35 | 3 | 32.5 |
TOTALS | 20 |
Step 2: Multiply the midpoint (x) by the frequency (f):
Frequency ( f ) | Midpoint ( x ) | Midpoint x * frequency f | |
---|---|---|---|
Between 5 and 10 | 1 | 7.5 | 7.5 |
10 ≤ t < 15 | 4 | 12.5 | 50 |
15 ≤ t < 20 | 6 | 17.5 | 105 |
20 ≤ t < 25 | 4 | 22.5 | 90 |
25 ≤ t < 30 | 2 | 27.5 | 55 |
30 ≤ t < 35 | 3 | 32.5 | 97.5 |
TOTALS | 20 | 405 |
Add up all of the totals for this step. In other words, add up all the values in the last column (you should get 405).
Step 3: Divide the last column (f*x) by the second column (f):
The mean of grouped data (x̄) = 405 / 20 = 20.25.
If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.
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wow i like this but please i need more examples on grouped data ….help me please
Glad it helped! What kinds of examples are you looking for? For example, a specific topic or for a specific class?
Thank you you really helped me in our assignment!
Tanx helped a lot
thank you