Question

the gas mileages (in miles per gallon) for 35 cars are shown in the frequency distribution. approximate the mean of the frequency distribution. the approximate mean of the frequency distribution is (round to one decimal place as needed.) gas mileage (in miles per gallon) frequency 26–29 10 30–33 14 34–37 4 38–41 7

Explanation:

Step1: Find midpoints of each class

For class 26–29: midpoint $x_1 = \frac{26 + 29}{2} = 27.5$
For class 30–33: midpoint $x_2 = \frac{30 + 33}{2} = 31.5$
For class 34–37: midpoint $x_3 = \frac{34 + 37}{2} = 35.5$
For class 38–41: midpoint $x_4 = \frac{38 + 41}{2} = 39.5$

Step2: Calculate $f_i \cdot x_i$ for each class

• For 26–29: $f_1 \cdot x_1 = 10 \times 27.5 = 275$
• For 30–33: $f_2 \cdot x_2 = 14 \times 31.5 = 441$
• For 34–37: $f_3 \cdot x_3 = 4 \times 35.5 = 142$
• For 38–41: $f_4 \cdot x_4 = 7 \times 39.5 = 276.5$

Step3: Find total of $f_i \cdot x_i$ and total frequency

Total of $f_i \cdot x_i$: $275 + 441 + 142 + 276.5 = 1134.5$
Total frequency $N = 10 + 14 + 4 + 7 = 35$

Step4: Calculate the mean

Mean $\bar{x} = \frac{\sum f_i \cdot x_i}{N} = \frac{1134.5}{35} \approx 32.4$

Answer:

32.4