Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean tothe actual mean of 52.3 degrees.

Answer 1

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:

`X_p=(42\cdot2+47\cdot4+52\cdot13+57\cdot4+62\cdot3)/(2+4+13+4+3)=52(5)/(13)=52.384`

3) So the mean of the frequency distribution is 52.4 (rounded off to the nerest ten).