Mean, Median, Mode Notes and Worksheets - Lindsay Bowden - Free Printable

Problem Analysis:

The task involves determining which measure of central tendency (mean, median, or mode) is most appropriate for each given data set. To solve this, we need to understand the characteristics of each measure:

1. Mean: The average value of a data set. It is sensitive to outliers.
2. Median: The middle value when the data is ordered. It is less affected by outliers.
3. Mode: The most frequently occurring value in the data set. It is useful for categorical or discrete data.

Step-by-Step Solution:

#### Definitions and Examples:
1. Outlier: A data point that is very different from the other data points.
- Example: \(7, 10, 13, 6, 229, 9, 8\). Here, 229 is an outlier.

2. Mean: Use when there are no outliers.
- Example: \(1, 3, 9, 5, 7, 8, 2, 3\). No extreme values.

3. Median: Use when there are outliers.
- Example: \(12, 108, 14, 15, 17, 13, 11\). The median is less affected by the outlier 108.

4. Mode: Use when your data can be put into categories.
- Example: Students voting for their favorite flavor of ice cream: chocolate, vanilla, vanilla, strawberry, chocolate, chocolate. The mode is "chocolate."

#### Examples: Determine the Best Measure for Each Data Set

1. Heights of small trees in feet:
\[
3.5, 4.8, 2.1, 5.6, 4.3, 3.9, 6.0, 5.9, 2.7, 4.9, 5.8, 3.5
\]
- Analysis: This data set contains numerical measurements with no obvious outliers. The mean would provide a good representation of the central tendency.
- Best Measure: Mean

2. Scores on a unit test:
\[
75, 78, 94, 87, 27, 93, 77, 83, 89, 90, 95, 81
\]
- Analysis: There is a low score (27) that could be considered an outlier. The median would be less affected by this outlier.
- Best Measure: Median

3. The price of milk at 6 different grocery stores:
\[
\$2.75, \$2.50, \$3.88, \$3.15, \$2.79, \$3.67
\]
- Analysis: This data set contains numerical measurements with no obvious outliers. The mean would provide a good representation of the central tendency.
- Best Measure: Mean

4. Favorite types of sandwiches:
\[
\text{pb&j, ham, turkey, ham, grilled cheese, pb&j, ham}
\]
- Analysis: This data set contains categorical data. The mode identifies the most common type of sandwich.
- Best Measure: Mode

5. Places the Olympic team won:
\[
\text{1st, 2nd, 1st, 3rd, 1st, 3rd, 2nd, 2nd, 1st, 1st}
\]
- Analysis: This data set contains ordinal data (ranks). The mode identifies the most frequent rank.
- Best Measure: Mode

6. Ages of students in a college art class:
\[
20, 54, 22, 23, 18, 19, 20, 18, 24, 25, 19, 20
\]
- Analysis: This data set contains numerical measurements with one high outlier (54). The median would be less affected by this outlier.
- Best Measure: Median

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \text{Mean} \\
2. & \text{Median} \\
3. & \text{Mean} \\
4. & \text{Mode} \\
5. & \text{Mode} \\
6. & \text{Median} \\
\end{array}
}
\]