Sure, let's break down the given problem step-by-step in solving it:
Step 1: Understanding the Data
Theo recorded the following data for his scores:
- Mean score for Language Arts: 98
- Mean score for Biology: 90
- Mean Absolute Deviation: 2
Step 2: Finding the Difference in the Means
To find the difference in the mean scores of Theo's Language Arts and Biology, we subtract the mean score of Biology from the mean score of Language Arts:
[tex]\[
\text{Difference in means} = \text{Mean score for Language Arts} - \text{Mean score for Biology}
\][/tex]
Substituting the given values:
[tex]\[
\text{Difference in means} = 98 - 90 = 8
\][/tex]
Step 3: Calculating the Ratio
Next, we need to find the ratio of the difference in the means to the mean absolute deviation. The formula for the ratio is:
[tex]\[
\text{Ratio} = \frac{\text{Difference in means}}{\text{Mean absolute deviation}}
\][/tex]
We substitute the values we have:
[tex]\[
\text{Ratio} = \frac{8}{2} = 4.0
\][/tex]
Summary:
- The difference in the means of Theo's scores in Language Arts and Biology is 8.
- The ratio of this difference to the mean absolute deviation is 4.0.
Therefore, the approximate ratio of the difference in the means to each of the mean absolute deviations is 4.0.
