Question

a sample of five words was randomly selected from a 200 - page book. the average number of letters of the five words was calculated. the process was repeated 10 times. the average word length of each of the 10 samples is given in the table.
what is the best estimate for the average word length in the whole book?
a 4.07 letters
b 4.15 letters
c 4.38 letters
d 4.49 letters

Explanation:

Step1: Recall the formula for the mean

The mean (average) of a set of data values $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 10$ and the data - values are the average word lengths of the 10 samples: $x_1=3.7,x_2 = 4.4,x_3=4.1,x_4=3.6,x_5=4.5,x_6=5.3,x_7=4.9,x_8=4.8,x_9=5.0,x_{10}=4.6$.

Step2: Calculate the sum of the data values

$\sum_{i=1}^{10}x_i=3.7 + 4.4+4.1+3.6+4.5+5.3+4.9+4.8+5.0+4.6=44.9$.

Step3: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{10}x_i}{10}=\frac{44.9}{10}=4.49$.

Answer:

D. 4.49 letters