Example: Your data set lists the number of books each student has read in the last month. After sorting, this is the data set: 3, 3, 5, 6, 6, 6, 8.
Example: Write “Number of Books” at the top of the first column. Write “Frequency” at the top of the second column. In the second row, write the first value under Number of Books: 3. Count the number of 3s in your data set. Since there are two 3s, write 2 underneath Frequency on the same row. Repeat for each value until you have the full chart: 3 | F = 2 5 | F = 1 6 | F = 3 8 | F = 1
Example: Our lowest value is 3. The number of students who read 3 books is 2. No one read fewer than that, so the cumulative frequency is 2. Add it to the first row of your chart: 3 | F = 2 | CF=2
Example: 3 | F = 2 | CF = 2 5 | F = 1 | CF = 2+1 = 3
Example: 3 | F = 2 | CF = 2 5 | F = 1 | CF = 2 + 1 = 3 6 | F = 3 | CF = 3 + 3 = 6 8 | F = 1 | CF = 6 + 1 = 7
Add all the individual frequencies together: 2 + 1 + 3 + 1 = 7, which is our final cumulative frequency. Count the number of data points. Our list was 3, 3, 5, 6, 6, 6, 8. There are 7 items, which is our final cumulative frequency.
Number of dogs: Discrete. There’s no such thing as half a dog. Depth of snow: Continuous. Snow gradually builds up, not in one unit at a time. If you tried to measure it in inches, you might find a snowdrifts that was 5. 6 inches deep.
Data set: 233, 259, 277, 278, 289, 301, 303 Chart (first column value, second column frequency, third column cumulative frequency): 200–250 | 1 | 1 251–300 | 4 | 1 + 4 = 5 301–350 | 2 | 5 + 2 = 7
For example, if your data set goes from 1 to 8, draw an x-axis with eight units marked on it. At each value on the x-axis, draw a point at the y-value that equals the cumulative frequency at that value. Connect each pair of adjacent points with a line. If there are no data points at a particular value, the absolute frequency is 0. Adding 0 to the last cumulative frequency doesn’t change its value, so draw a point at the same y-value as the last value. Because cumulative frequency always increases along with the values, your line graph should always stay steady or go up as it moves to the right. If the line goes down at any point, you might be looking at absolute frequency by mistake.
Look at the last point on the far right of your graph. Its y-value is the total cumulative frequency, which is the number of points in the data set. Let’s say this value is 16 Multiply this value by ½ and find it on the y-axis. In our example, half of 16 is 8. Find 8 on the y-axis. Find the point on the line graph at this y-value. Move your finger from the 8 on the y-axis out across the graph. Stop when your finger touches the line of your graph. This is the point where exactly half of your data points have been counted. Find the x-axis at this point. Move your finger straight down to see the x-axis value. This value is the median of your data set. For example, if this value is 65, then half of your data set is below 65, and half is above 65.
To find the lower quartile’s y-axis value, take the maximum cumulative frequency and multiply by ¼. The corresponding x-value tells you the value with exactly ¼ of the data below it. To find the upper quartile’s y-axis value, multiply the maximum cumulative frequency by ¾. The corresponding x-value tells you the value with exactly ¾ of the data below it and ¼ above it.
