Question

find the mean for the data items in the given frequency distribution.
the mean is (round to 3 decimal places as needed.)

Explanation:

Step1: Calculate the product of each score and its frequency

For \(x = 1\) and \(f=2\): \(1\times2 = 2\)
For \(x = 2\) and \(f = 2\): \(2\times2=4\)
For \(x = 3\) and \(f = 6\): \(3\times6 = 18\)
For \(x = 4\) and \(f = 3\): \(4\times3=12\)
For \(x = 5\) and \(f = 4\): \(5\times4 = 20\)
For \(x = 6\) and \(f = 6\): \(6\times6=36\)
For \(x = 7\) and \(f = 3\): \(7\times3 = 21\)
For \(x = 8\) and \(f = 1\): \(8\times1=8\)

Step2: Sum up the products

\(\sum(x\times f)=2 + 4+18+12+20+36+21+8=121\)

Step3: Calculate the total frequency

\(\sum f=2 + 2+6+3+4+6+3+1=27\)

Step4: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum(x\times f)}{\sum f}\)
\(\bar{x}=\frac{121}{27}\approx4.481\)

Answer:

\(4.481\)