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So if you want to use images instead of bars, you should scale by the square root instead if the original area is w × h = wh, scaling by 3 makes 3w × 3h =9wh, but scaling by √3 makes w(√3) × h(√3) = 3wh
This could work if it's understood the area represents the value. In bar charts it's the height which represents the value, which is why it's very important the widths are uniform. But certainly an area approach could be used to make a fun and honest chart - but it wouldn't be a bar chart.
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So if you want to use images instead of bars, you should scale by the square root instead
if the original area is w × h = wh, scaling by 3 makes 3w × 3h =9wh, but scaling by √3 makes w(√3) × h(√3) = 3wh
This could work if it's understood the area represents the value. In bar charts it's the height which represents the value, which is why it's very important the widths are uniform. But certainly an area approach could be used to make a fun and honest chart - but it wouldn't be a bar chart.