Question

the table shows the frequencies of the data values for four data sets. which data set has the greatest mean?
(a) data set a
(b) data set b
(c) data set c
(d) data set d

Explanation:

Step1: Calculate the mean of Data set A

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}\).
For Data set A:

$$
LATEXBLOCK0
$$

$$ \sum_{i = 1}^{n}f_{i}=1 + 1+3 + 7=12 $$

\(\bar{x}_{A}=\frac{592}{12}\approx49.33\)

Step2: Calculate the mean of Data set B

For Data set B:

$$
LATEXBLOCK1
$$

$$ \sum_{i = 1}^{n}f_{i}=1+2 + 3+7=13 $$

\(\bar{x}_{B}=\frac{636}{13}\approx48.92\)

Step3: Calculate the mean of Data set C

For Data set C:

$$
LATEXBLOCK2
$$

$$ \sum_{i = 1}^{n}f_{i}=7+2 + 2+1=12 $$

\(\bar{x}_{C}=\frac{516}{12}=43\)

Step4: Calculate the mean of Data set D

For Data set D:

$$
LATEXBLOCK3
$$

$$ \sum_{i = 1}^{n}f_{i}=7+3 + 1+1=12 $$

\(\bar{x}_{D}=\frac{512}{12}\approx42.67\)

Answer:

A. Data set A