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 \(x\) and \(f\)

For each row, we calculate \(x\times f\):

• When \(x = 1,f=3\), \(x\times f=1\times3 = 3\)
• When \(x = 2,f = 3\), \(x\times f=2\times3=6\)
• When \(x = 3,f = 2\), \(x\times f=3\times2 = 6\)
• When \(x = 4,f = 6\), \(x\times f=4\times6=24\)
• When \(x = 5,f = 4\), \(x\times f=5\times4 = 20\)
• When \(x = 6,f = 9\), \(x\times f=6\times9=54\)
• When \(x = 7,f = 8\), \(x\times f=7\times8=56\)
• When \(x = 8,f = 6\), \(x\times f=8\times6 = 48\)
• When \(x = 9,f = 6\), \(x\times f=9\times6=54\)
• When \(x = 10,f = 3\), \(x\times f=10\times3=30\)

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

\(\sum(x\times f)=3 + 6+6+24+20+54+56+48+54+30\)
\(=301\)
\(\sum f=3 + 3+2+6+4+9+8+6+6+3\)
\(=50\)

Step3: Calculate the mean \(\bar{x}\)

The formula for the mean of a frequency - distribution is \(\bar{x}=\frac{\sum(x\times f)}{\sum f}\)
Substitute \(\sum(x\times f) = 301\) and \(\sum f=50\) into the formula:
\(\bar{x}=\frac{301}{50}=6.02\)

Answer:

\(6.020\)