How to tell if there is equal variance in a box plot? I'm trying to decide if the variance in these groups in this boxplot are equal, so how can I tell how much variation each group has just looking at the box plot? And how can I tell if they all have equal variance?
Here is the boxplot:

 A: A boxplot illustrates the range and the interquartile range (IQR), both of which are measures of the variation in a data set. Generally the range is considered to be too easily influenced by extreme values, so the IQR is preferred.
In the data sets above, we can say the following:
Ford, Nissan, Toyota and Volkswagen have similar IQR, so have similar variation (not variance).
Honda and Mitsubishi have similar IQR to each other, which is less than that of the previous group.
You can, however, estimate the variance from a boxplot.
Let me consider the Toyota data.
We have (very roughly):
Smallest value:  400
Lower quartile:  650
Median:          850
Upper quartile: 1200
Largest value:  1500

Although we don't know the sample size, we can still construct a grouped frequency table for the data, with f=25 (25%) for each of the quarters:
          interval    frequency (f)  mid-value (x)    fx        fx^2
         400 to  650       25           525          13125     6890625
         650 to  850       25           750          18750    14062500
         850 to 1200       25          1025          25625    26265625
        1200 to 1500       25          1350          33750    45562500
        --------------------------------------------------------------
        Totals            100                        91250    92781250

These can be used to estimate the mean as 912.5 and the variance as 95156.
