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: Determine the mid - point and frequency for each class

We assume the classes are: 2 - 3 (mid - point $x_1 = 2.5$, frequency $f_1=3$), 4 - 5 (mid - point $x_2 = 4.5$, frequency $f_2 = 1$), 6 - 7 (mid - point $x_3=6.5$, frequency $f_3 = 1$), 8 - 9 (mid - point $x_4 = 8.5$, frequency $f_4=1$), 10 (mid - point $x_5 = 10$, frequency $f_5 = 3$).

Step2: Calculate the product of mid - point and frequency for each class

$x_1f_1=2.5\times3 = 7.5$, $x_2f_2=4.5\times1 = 4.5$, $x_3f_3=6.5\times1 = 6.5$, $x_4f_4=8.5\times1 = 8.5$, $x_5f_5=10\times3 = 30$.

Step3: Calculate the sum of the products

$\sum_{i = 1}^{5}x_if_i=7.5 + 4.5+6.5 + 8.5+30=57$.

Step4: Calculate the total frequency

$\sum_{i = 1}^{5}f_i=3 + 1+1+1+3=9$.

Step5: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{5}x_if_i}{\sum_{i = 1}^{5}f_i}=\frac{57}{9}\approx6.33$.

Answer:

$6.33$