A company wants to monitor the amount of money spent by their employees on stationery
each month. The box plot below shows information about the distribution of money spent on
stationery by some male employees over a month. a) Calculate the range and
interquartile range for the amounts of money spent by these male employees.
To calculate the range, what we’re actually gonna do is we’re gonna have to take the
lowest value away from the highest value. And if we look at the box plot, what we’ve got is the highest value, is at top end of
the box plot which is at 22 and our lowest value is at the bottom end of the box
plot which is at four. So the range is gonna be equal to 22 minus 4 which gives an answer of 18 pounds.
Okay, great, so that’s the range. Now, we need to move on to the interquartile range. So now, if we look at the centre section of our box plot, what we have is the upper
quartile, is the top line within that centre section and the bottom line is our
lower quartile. And if we then go down and read off the box plot, we can actually see that the upper
quartile is gonna be equal to 18 and the lower quartile is gonna be equal to 12.
And the formula for actually calculating the interquartile range is the upper
quartile minus the lower quartile. So therefore, the interquartile range is gonna be equal to 18, which is the upper
quartile, minus 12, our lower quartile, which gives us an answer of six pounds. So that’s part a solved. Now, we can move on to part b.
Okay, for part b, we actually get some extra information. We got the table below shows information about the distribution of money spent by
some female employees over a month. So we’ve got the money spent: the smallest is three pounds, the lower quartile is
eight pounds, the median is 14 pounds, the upper quartile is 20 pounds, the largest
is 24 pounds.
Part b) On the grid above, draw the box plot for the information in the table.
So first of all, what we’re gonna do is actually draw the smallest value and I’ve
shown that here with the small line I’ve drawn at three because three is the
smallest value. Next, I’ve actually drawn the largest value which is here at 24. Then, next, I’ve drawn the lower quartile at eight, the median at 14, and then
finally the upper quartile at 20. And then, I joined them together in the same way that the previous box plot was
actually joined together.
So we’ve now got the box plot which actually shows the distribution of money spent by
the female employees. It’s worth noting at this point that actually the height doesn’t matter. But I’ve just used the same scale as the other box plot. So now, that’s part a and part b are answered, we’re gonna move on to part c.
Muhammed says, “The box plot shows that male employees spend more money than female
employees.” c) Is Muhammad correct? Give a reason for your answer.
Well, in this part of the question, Muhammad is talking about spending more money and
whether it’s males or females. So therefore, what we’re actually gonna be looking at is the median of each of our
box plots. So therefore, we can actually answer the question because we can see that the male
employees’s median is 16 and the female employees’s median is 14. So therefore, is Muhammad correct? Well, yes because the male employees have a greater median.