Question

pre-algebra ic sem 2 fall 2025
comparing measures of center
and variability
this week
last week
step 1
find the mean.
find the mean.
\\( \frac { 42 + 38 + 45 + 46 + 39 } { 5 } = 42 \\)
\\( \frac { 56 + 58 + 52 + 62 + 62 } { 5 } = 58 \\)
step 2
find the mean absolute
deviation.
find the mean absolute
deviation.
\\( \frac { | 42 - 42 | + | 38 - 42 | + | 45 - 42 | + | 46 - 42 | } { 5 } \\)
\\( \frac { | 56 - 58 | + | 52 - 58 | + | 62 - 58 | } { 5 } \\)
step 3
find the ratio of the
differences of the means
compared to the mean
absolute deviation.
find the ratio of the
differences of the means
compared to the mean
absolute deviation.
\\( \frac { 42 } { 2.8 } = 15 \\)
\\( \frac { 58 } { 3.2 } = 18.1.25 \\)
step 4
the difference in the means is about \\( \frac { 15 + 18 } { 2 } = 16.5 \\)
times the mean absolute deviations.
in which step did daniela make the first error?

Explanation:

Step1: Check Step 1

Calculate the mean for "This Week": \(\frac{42 + 38+45 + 46+39}{5}=\frac{210}{5} = 42\). Calculate the mean for "Last Week": \(\frac{56+58 + 52+62+62}{5}=\frac{290}{5}=58\). Step 1 is correct.

Step2: Check Step 2

For "This Week": \(\frac{|42 - 42|+|38 - 42|+|45 - 42|+|46 - 42|+|39 - 42|}{5}=\frac{0 + 4+3 + 4+3}{5}=\frac{14}{5}=2.8\). For "Last Week": \(\frac{|56 - 58|+|58 - 58|+|52 - 58|+|62 - 58|+|62 - 58|}{5}=\frac{2+0 + 6+4+4}{5}=\frac{16}{5}=3.2\). Step 2 is correct.

Step3: Check Step 3

The formula for the ratio of the differences of the means compared to the mean absolute deviation is \(\frac{\text{Difference of means}}{\text{Mean Absolute Deviation}}\). The difference of means is \(|42 - 58|=16\). The correct ratios should be \(\frac{16}{2.8}\approx5.71\) (using "This Week" MAD) and \(\frac{16}{3.2} = 5\) (not \(\frac{42}{2.8}\) and \(\frac{58}{3.2}\) as done in the original Step 3). So, Step 3 is incorrect.

Answer:

Step 3