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All courses Algebra I · S-ID.2 38 of 76
Compare data sets using center and spread measures appropriate to distribution shape.

Find the mean of two data sets and compare the means

Problem
Find the mean of each data set, then compare them: data set \(A~=~4,~6,~8\); data set \(B~=~5,~5,~11\).
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Hint

Add the values in each data set first, then divide each sum by the number of values.

The mean is \(sum of the data / number of data values\).

Solution walkthrough

01

Compute the mean of data set A

\[\text{mean}~A=(4+6+8)/3=18/3=6\]

Data set A has three values whose sum is 18.

02

Compute the mean of data set B

\[\text{mean}~B=(5+5+11)/3=21/3=7\]

Data set B also has three values, and their sum is 21.

03

Compare the centers

\[7-6=1\]

Data set B's mean exceeds data set A's mean by 1.

04

State both means and the comparison

\[\text{Data}~\text{set}~A~\text{has}~\text{mean}~6~\text{and}~\text{data}~\text{set}~B~\text{has}~\text{mean}~7,~\text{so}~\text{data}~\text{set}~B~\text{has}~\text{the}~\text{larger}~\text{mean}~by~1.\]

The result answers both calculation and comparison parts of the prompt.

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Another way

  1. Balance A around 6 directly; for B, redistribute one unit from 11 to each 5 to obtain 6,6,9, then one more balanced unit per value gives mean 7.

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Common mistake

Do not compare the sums 18 and 21 as if they were means. Divide each sum by its three observations.

Solution walkthrough video