Frequency distribution is arrangement of data in a table format where each entry displays the frequency of occurrence of each of the values.
A frequency distribution of data can be represented in the form of frequency tables, histograms or bar charts.
Grade 5 has 9 students and last week they got their math performance report. The scores obtained were:
90, 80, 60, 20, 40, 50, 70, 90
The frequency distribution table for the above data will be:
| Scores | Tally marks | Frequency(f) |
|---|---|---|
| 90 | || | 2 |
| 80 | | | 1 |
| 60 | | | 1 |
| 20 | | | 1 |
| 40 | | | 1 |
| 50 | | | 1 |
| 70 | | | 1 |
Steps to determine frequency distribution:
1. Determine the minimum and maximum values.
Here,
Minimum value is 1
Maximum value is 6
2. Use tally marks to record the frequency of heads.
| No. of coins tossed | Tally Marks | Frequency of heads |
|---|---|---|
| 1 | || | |
| 2 | |||| ||| | |
| 3 | |||| | | |
| 4 | |||| | | |
| 5 | ||| | |
| 6 | ||| |
3. Count the tally marks to find the frequency of heads.
| No. of coins tossed | Tally Marks | Frequency of heads |
|---|---|---|
| 1 | || | 2 |
| 2 | |||| ||| | 7 |
| 3 | |||| | | 5 |
| 4 | |||| | | 5 |
| 5 | ||| | 3 |
| 6 | ||| | 3 |
1. Find the minimum and maximum value
Here,
Minimum value is 4
Maximum value is 67
2. Calculate the range
Range=Maximum- Minimum
67 - 4 = 63
The range is 63
3. Calculate group size.
Divide the range by number of groups, then round up that group size
So, 64/10 is 6.4
6.4 rounded to its nearest integer value (that is greater than 6.4) is 7
4. Select a starting value.
Choose the lowest number from the group or select 0.
5. Form groups.
Create a list of groups and put them in the first column, which is the data groups or class intervals.Make sure the end value of each group is less than the start value of the next group.
| Class Intervals | Tally Marks | Frequency of heads |
|---|---|---|
| 0-9 | ||
| 10-19 | ||
| 20-29 | ||
| 30-39 | ||
| 40-49 | ||
| 50-59 | ||
| 60-69 |
6. Get the upper and lower limits for each group.
7. Use tally marks to record the observations.
| Class Intervals | Tally Marks | Frequency of heads |
|---|---|---|
| 0-9 | || | |
| 10-19 | |||| || | |
| 20-29 | |||| |||| | |
| 30-39 | |||| |||| | | |
| 40-49 | |||| |||| | |
| 50-59 | |||| | | |
| 60-69 | || |
8. Count the tally marks for each group.
After counting, write the corresponding frequency in the frequency column.
| Class Intervals | Tally Marks | Frequency of heads |
|---|---|---|
| 0-9 | || | 2 |
| 10-19 | |||| || | 6 |
| 20-29 | |||| |||| | 8 |
| 30-39 | |||| |||| | | 9 |
| 40-49 | |||| |||| | 8 |
| 50-59 | |||| | | 5 |
| 60-69 | || | 2 |
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