4 mistakes learners make with cumulative frequency and histograms, each one named and explained.
Both graphs are read off the axis they were built from: the total frequency on one, and frequency density on the other.
The class widths are unequal and you draw the bar heights as the frequencies.
Every bar chart so far has used frequency for height, and the bars still look right.
Question. A histogram has classes of different widths. What goes on the vertical axis?
A common answer. frequency
The answer. frequency density, which is frequency divided by class width
Why. With unequal widths it is the area of each bar that represents the frequency, not its height.
Check the widths first. If they differ, divide before you plot.
The axis runs to 100 but there are 80 people, and you read the median across from 50.
The axis label is the number in front of you, and it is usually a round number.
Question. A cumulative frequency graph has 80 people, on an axis drawn to 100. Where do you read the median?
A common answer. across from 50
The answer. across from 40
Why. The median is halfway through the data, so halve the total frequency, not the axis.
Find the top of the curve, not the top of the axis. Halve that.
You count to the middle of the numbers as they were written down and call it the median.
Counting to the middle is the method, and the list already looks like a list.
Question. To find the median of a list of numbers, what has to happen first?
A common answer. nothing, count to the middle
The answer. put the list in order
Why. The median is the middle value by size, so the order they were written in does not matter.
Sort first, every time. Then count.
You plot each running total against the middle of its class.
Midpoints are what you plot for an estimated mean and for a frequency polygon, so the habit carries over.
Question. On a cumulative frequency graph, what do you plot the running total against?
A common answer. the midpoint of the class
The answer. the upper boundary of the class
Why. The running total counts everything up to the end of that class, so it belongs at the end.
Ask what the total includes. It includes everything up to the top of the class.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.