Frequency distribution

The following frequency distribution gives the time spent for a 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. Please 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

Final Answer:

m =  10.8706 min

Step-by-step explanation:

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

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