I'm really confused because for question 5 the solution says "Looking at areas under the curve $Q_1$ appears to be around 20, the median is around 30 and $Q_3$ is about 40."
I don't know what they are talking about with the area under the curve. I know the distribution is symmetric and looks normal so that's why I would assume the median is 30, etc..
But I cannot apply the same logic to question 6, in which case I have to use this "area under the curve" idea. I don't see how I can evenly break up all the bars into even squares to then see how many squares are in each bar and therefore how much area one bar takes up.
For question 6, the solution is "Looking at areas under the curve, $Q_1$ appears to be around 10, the median is around 30 and $Q_3$ is about 50.
Best Answer
Both given histograms are symmetric with respect to $30$. So, the median (the central value) of the data must lie by $30$.
The box of the boxplot stands for around $50\%$ of the data (the mass of data from the lower to the upper quartile).
Looking at the first diagram and comparing the sizes of the bars you see that in the first histogram about $50\%$ of the data spreads from $20$ to $40$. So, boxplot $B$ is correct.
Similarly, in the second histogram about $50\%$ of the data spreads from $10$ to $50$. So, boxplot $C$ is correct.