Data and Displays · Challenge problem

A histogram of $40$ whole-number test scores has bins $0$–$9$: $6$, $10$–$19$: $8$, $20$–$29$: $12$, $30$–$39$: $8$, $40$–$49$: $6$. The midpoint estimate of the mean is $24.5$. If instead every score is assumed to sit at the bottom of its bin, what is the estimated mean?