Frequency distribution

The following frequency distribution gives the time spent for fill-up at a gas station.  Assume that each value in a class is equal to the midpoint of the class.  Estimate the mean fill-up time for the given data.  Round your answer to the nearest hundredth.

Time for Fill-Up at Gas Station (In Minutes)	Frequency
8.50-9.49	52
9.50-10.49	47
10.50-11.49	22
11.50-12.49	51
12.50-13.49	37

Correct answer:

m =  10.8706 min

Step-by-step explanation:

$$\begin{gathered} a=(9.49+8.50)\mathrm{/}2={\displaystyle \frac{1799}{200}}=8.995\text{ min } \\ b=(10.49+9.50)\mathrm{/}2={\displaystyle \frac{1999}{200}}=9.995\text{ min } \\ c=(11.49+10.50)\mathrm{/}2={\displaystyle \frac{2199}{200}}=10.995\text{ min } \\ d=(12.49+11.50)\mathrm{/}2={\displaystyle \frac{2399}{200}}=11.995\text{ min } \\ e=(13.49+12.50)\mathrm{/}2={\displaystyle \frac{2599}{200}}=12.995\text{ min } \\ m={\displaystyle \frac{a\cdot 52+b\cdot 47+c\cdot 22+d\cdot 51+e\cdot 37}{52+47+22+51+37}}={\displaystyle \frac{8.995\cdot 52+9.995\cdot 47+10.995\cdot 22+11.995\cdot 51+12.995\cdot 37}{52+47+22+51+37}}=10.8706\text{ min} \end{gathered}$$

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