Exam Scores The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivan’s College Algebra course.





(c) Determine the mean and median score.

Verified step by step guidance

1. Step 1: Organize all the homework scores into a single list by reading each row and column from the table. This will give you a complete data set of all the scores.
2. Step 2: To find the mean score, use the formula for the mean: \(\text{Mean} = \frac{\sum \text{scores}}{\text{number of scores}}\). Add all the scores together and then divide by the total number of scores.
3. Step 3: To find the median score, first arrange all the scores in ascending order from smallest to largest.
4. Step 4: Determine the position of the median using the formula \(\text{Median position} = \frac{n+1}{2}\), where \(n\) is the total number of scores. If \(n\) is odd, the median is the score at this position. If \(n\) is even, the median is the average of the two middle scores.
5. Step 5: Identify the median score from the ordered list using the position found in Step 4. This value represents the middle score of the data set.

Key Concepts

Mean (Arithmetic Average)

The mean is the sum of all data values divided by the number of values. It provides a measure of central tendency that represents the average score in a data set. The mean is sensitive to extreme values (outliers), which can affect its value.

Median

The median is the middle value when the data set is ordered from smallest to largest. It divides the data into two equal halves and is a measure of central tendency less affected by outliers or skewed data than the mean.

Data Organization and Ordering

Organizing data in ascending order is essential for accurately finding the median. Properly arranging the scores helps identify the middle value and ensures correct calculation of statistical measures like mean and median.