Question

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 56.1 degrees. low temperature (°f) 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 frequency 3 6 10 7 2 the mean of the frequency distribution is degrees. (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Find mid - points

For the interval \(40 - 44\), mid - point \(x_1=\frac{40 + 44}{2}=42\); for \(45 - 49\), \(x_2=\frac{45+49}{2}=47\); for \(50 - 54\), \(x_3=\frac{50 + 54}{2}=52\); for \(55 - 59\), \(x_4=\frac{55+59}{2}=57\); for \(60 - 64\), \(x_5=\frac{60 + 64}{2}=62\).

Step2: Calculate the product of mid - points and frequencies

\(f_1x_1=3\times42 = 126\), \(f_2x_2=6\times47 = 282\), \(f_3x_3=10\times52=520\), \(f_4x_4=7\times57 = 399\), \(f_5x_5=2\times62 = 124\).

Step3: Find the sum of frequencies and the sum of \(f_ix_i\)

\(\sum f_i=3 + 6+10 + 7+2=28\), \(\sum f_ix_i=126+282 + 520+399+124 = 1451\).

Step4: Calculate the mean

The mean \(\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{1451}{28}\approx51.8\).

Answer:

\(51.8\)