Question

mathematics. math 003 fall 2025
ework; unit 4 - mean, median and mode, and ability
question 16, 7.3.41 part 1 of 3
hw score: 47.83%, 22 of 46 points
points: 0 of 1
use the frequency - distribution table to find the a. mean, b. median, and c. mode.
data item frequency data item frequency
3 1 6 4
4 1 7 7
5 3 8 3
a. the mean is
(type a whole number or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Calculate sum of data - frequency products

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$.
For data - item $x_1 = 3$ with frequency $f_1=1$, product is $3\times1 = 3$.
For $x_2 = 4$ and $f_2 = 1$, product is $4\times1=4$.
For $x_3 = 5$ and $f_3 = 3$, product is $5\times3 = 15$.
For $x_4 = 6$ and $f_4 = 4$, product is $6\times4=24$.
For $x_5 = 7$ and $f_5 = 7$, product is $7\times7 = 49$.
For $x_6 = 8$ and $f_6 = 3$, product is $8\times3=24$.
The sum of products $\sum_{i = 1}^{6}x_if_i=3 + 4+15 + 24+49+24=119$.

Step2: Calculate total frequency

The total frequency $\sum_{i = 1}^{6}f_i=1 + 1+3 + 4+7+3=19$.

Step3: Calculate the mean

$\bar{x}=\frac{119}{19}\approx6.3$.

Answer:

$6.3$