Question

section 3.3 homework
score: 4/8 answered: 4/8
question 5
approximate the sample mean for the following frequency distribution.

data	frequency
29 - 32	5
33 - 36	6
37 - 40	12
41 - 44	8

sample mean =
report answer accurate to one decimal place.

Explanation:

Step1: Find the mid - points of each class

For the class $25 - 28$, the mid - point $x_1=\frac{25 + 28}{2}=26.5$.
For the class $29 - 32$, the mid - point $x_2=\frac{29+32}{2}=30.5$.
For the class $33 - 36$, the mid - point $x_3=\frac{33 + 36}{2}=34.5$.
For the class $37 - 40$, the mid - point $x_4=\frac{37+40}{2}=38.5$.
For the class $41 - 44$, the mid - point $x_5=\frac{41 + 44}{2}=42.5$.

Step2: Calculate the product of mid - points and frequencies

$f_1x_1=1\times26.5 = 26.5$.
$f_2x_2=5\times30.5 = 152.5$.
$f_3x_3=6\times34.5 = 207$.
$f_4x_4=12\times38.5 = 462$.
$f_5x_5=8\times42.5 = 340$.

Step3: Calculate the sum of frequencies

$n=\sum_{i = 1}^{5}f_i=1 + 5+6 + 12+8=32$.

Step4: Calculate the sum of the products

$\sum_{i = 1}^{5}f_ix_i=26.5+152.5 + 207+462+340=1188$.

Step5: Calculate the sample mean

The sample mean $\bar{x}=\frac{\sum_{i = 1}^{5}f_ix_i}{n}=\frac{1188}{32}=37.125\approx37.1$.

Answer:

$37.1$