Question

the graph below represents the result of a survey in which a number of students reported how many letters were in their last names. name length what was the mean name length?

Explanation:

Step1: Calculate the total number of letters

Multiply the number of letters by the frequency for each bar:

• For \(3\) letters: \(3\times3 = 9\)
• For \(4\) letters: \(4\times6=24\)
• For \(5\) letters: \(5\times3 = 15\)
• For \(6\) letters: \(6\times3=18\)
• For \(8\) letters: \(8\times2 = 16\)
• For \(9\) letters: \(9\times1=9\)
• For \(10\) letters: \(10\times2=20\)

Sum these values: \(9 + 24+15 + 18+16+9+20=\sum x\times f=111\)

Step2: Calculate the total number of students

Sum the frequencies: \(3 + 6+3 + 3+2+1+2=\sum f=20\)

Step3: Calculate the mean

Use the formula for the mean \(\bar{x}=\frac{\sum x\times f}{\sum f}\)

\(\bar{x}=\frac{111}{20}=5.55\)

Answer:

\(5.55\)