Video Transcript
The following table represents the
speed of the members of a cycling club over a long-distance race. David drew a histogram to represent
this data. What is the mistake in this
histogram?
Here we have a table that shows us
the speed of members of a cycling club. We’re shown a histogram of this
data. And we can recall that in a
histogram, we don’t plot frequency on the 𝑦-axis. But instead we plot frequency
density, just like David did. In order to find the frequency
density, we calculate the frequency divided by the class width. In order to calculate the frequency
density of our first class interval, we could quickly subtract it from five to give
us three. We could also see that the values
six, seven, and eight miles per hour would be in this interval. We can’t include the value of five
miles per hour because of the inequality here that the speed has to be greater than
five.
As the class width is three here,
to find the frequency density, we take our frequency of 12 and divide by the class
width of three, which gives us a frequency density of four. If we take a quick look at the
histogram, we can see that David correctly drew the interval from five to eight. And the frequency density was
correct with a value of four. In the second column, we have the
inequality that eight is less than 𝑠 is less than or equal to 10, where 𝑠 is the
speed. In this case, we’d have the values
of nine and 10, giving us a class width of two. The frequency density would be the
frequency of 24 divided by the class width of two, which gives us a density of
12. This bar is correct on the
histogram.
We can find the next frequency
density by dividing our frequency by five, which was our class width, to give us
seven. This is correctly given on David’s
histogram. The final three frequency densities
can be calculated as four, one, and one. If we look at our histogram, we can
see that our fourth bar is correct and so is the final one. But this one is not. So what is the mistake? Well, he drew his interval going up
to a height of 10, which would be the frequency. We could give our answer that the
bar of the interval 20 is less than 𝑠 is less than or equal to 30 represents the
frequency instead of the frequency density.
