52.4
1) Considering that we have grouped data, we need to the middle point from each interval by calculating the average from the lower value and the higher value from each row:
Low Temperature (ºF) | frequency | Middle Point
---------------------------------
40-44 2 (40+44)/2=42
45-49 4 (45+49)/2=47
50-54 13 (50+54)/2=52
55-59 4 (55+59)/2=57
60-64 3 (60+64)/2=62
2) So now, we can find the weighted mean since we have the frequencies:
[tex]X_p=\frac{42\cdot2+47\cdot4+52\cdot13+57\cdot4+62\cdot3}{2+4+13+4+3}=52\frac{5}{13}=52.384[/tex]3) So the mean of the frequency distribution is 52.4 (rounded off to the nerest ten).