Questions: Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 52.1 degrees. Low Temperature (oF) 40-44 45-49 50-54 55-59 60-64 Frequency 1 6 10 4 3 The mean of the frequency distribution is degrees. (Round to the nearest tenth as needed.)

Solution Steps

• For the range 40-44, the midpoint is calculated as $\frac{40 + 44}{2} = 42$.

• For the range 45-49, the midpoint is calculated as $\frac{45 + 49}{2} = 47$.

• For the range 50-54, the midpoint is calculated as $\frac{50 + 54}{2} = 52$.

• For the range 55-59, the midpoint is calculated as $\frac{55 + 59}{2} = 57$.

• For the range 60-64, the midpoint is calculated as $\frac{60 + 64}{2} = 62$.

• The midpoint 42 is multiplied by its frequency 1 to get 42.

• The midpoint 47 is multiplied by its frequency 6 to get 282.

• The midpoint 52 is multiplied by its frequency 10 to get 520.

• The midpoint 57 is multiplied by its frequency 4 to get 228.

• The midpoint 62 is multiplied by its frequency 3 to get 186.

The sum of all weighted values is $\sum([42, 282, 520, 228, 186]) = 1258$.

The total frequency is $\sum([1, 6, 10, 4, 3]) = 24$.

The mean of the frequency distribution is calculated as $\frac{\text{Sum of Products}}{\text{Total Frequency}} = \frac{1258}{24} = 52.4$.

Final Answer: The mean of the frequency distribution is 52.4.