Question

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 50.2 degrees
low temperature (°f) 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64
frequency 3 7 10 4 1
the mean of the frequency distribution is degrees
(type an integer or decimal rounded to one decimal place as needed)

Explanation:

Step1: Find the mid - point of each class

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

Step2: Calculate \(\sum(f\times x)\) and \(\sum f\)

Let \(f_1 = 3\), \(f_2=7\), \(f_3 = 10\), \(f_4=4\), \(f_5 = 1\).
\(\sum(f\times x)=f_1x_1+f_2x_2+f_3x_3+f_4x_4+f_5x_5\)
\(=3\times42+7\times47 + 10\times52+4\times57+1\times62\)
\(=126+329+520+228+62\)
\(=1265\)
\(\sum f=3 + 7+10+4+1=25\)

Step3: Calculate the mean

The formula for the mean of a frequency distribution is \(\bar{x}=\frac{\sum(f\times x)}{\sum f}\)
\(\bar{x}=\frac{1265}{25}=50.6\)

Answer:

\(50.6\)