Question

name length
what was the mean name length?

Explanation:

Step1: Recall the mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$, where $x_i$ is the value and $f_i$ is the frequency.

Step2: Calculate the numerator $\sum_{i = 1}^{n}x_if_i$

For $x_1 = 2,f_1=1$; $x_2 = 3,f_2 = 5$; $x_3=4,f_3 = 2$; $x_4=5,f_4 = 1$; $x_5=6,f_5 = 2$; $x_6=7,f_6 = 1$; $x_7=8,f_7 = 2$; $x_8=9,f_8 = 3$; $x_9=10,f_9 = 3$.
$\sum_{i = 1}^{n}x_if_i=2\times1 + 3\times5+4\times2+5\times1+6\times2+7\times1+8\times2+9\times3+10\times3$
$=2 + 15+8+5+12+7+16+27+30$
$=122$.

Step3: Calculate the denominator $\sum_{i = 1}^{n}f_i$

$\sum_{i = 1}^{n}f_i=1 + 5+2+1+2+1+2+3+3$
$=20$.

Step4: Calculate the mean

$\bar{x}=\frac{122}{20}=6.1$.

Answer:

$6.1$