Answer:
1. The mean of the data summarized in the given frequency distribution is 51.81 degrees
2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.
Explanation:
1) We are given a Frequency distribution.
Mean of a frequency distribution = Fx/F
Where
Fx = Frequency × midpoint
Low Temperature (◦F) Frequency
40−44 2
45−49 7
50−54 9
55−59 6
60−64 2
F =Total Frequency
= 2 + 7 + 9 + 6 + 2
= 26
a)For low temperature 40 - 44
Frequency = 2
Midpoint (x) = 40 +44/2 = 42
Fx =42 × 2 = 84
b) For low temperature 45 - 49
Frequency = 2
Midpoint (x) = 45+49/2 = 47
Fx =47 × 7 = 329
For low temperature 50 - 54
Frequency = 2
Midpoint (x) = 50 + 54/2 = 52
Fx =52 × 9 = 468
For low temperature 55 - 59
Frequency = 6
Midpoint (x) = 55 + 59/2 = 57
Fx =57 × 6 = 342
For low temperature 60 - 64
Frequency = 2
Midpoint (x) = 60 +64/2 = 62
Fx =62 × 2 = 124
Total Fx =84 + 329 + 468 + 342 + 124
= 1347
Mean =Total Fx/ Total Frequency
= 1347/26
= 51.807692308
Approximately = 51.81 degrees
Therefore, mean of the data summarized in the given frequency distribution is 51.81 degrees
2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.