Question

The top ten scores on Mr. Yunker's science test were \(98,96,95,100,93,95,95,96,94\), and 97 . What is the median of this set of data? (Statistics Review) (A) \(95.9\) (B) \(95.5\) (C) \(95.0\) (D) \(94.9\)

Short answer

The median is 95.5 (Option B).

Step-by-step solution

Organize the Data

First, list the scores in numerical order so that we can find the median. The scores are: 93, 94, 95, 95, 95, 96, 96, 97, 98, 100.

Identify the Middle Value(s)

Since there are 10 scores (an even number), the median will be the average of the 5th and 6th scores. Count to the 5th and 6th scores in the ordered list: 93, 94, 95, (5th: 95), (6th: 96), 96, 97, 98, 100.

Calculate the Median

The median is the average of the 5th and 6th scores, which are both 95 and 96, respectively. Calculate the median: \[ \text{Median} = \frac{95 + 96}{2} = 95.5. \]

Key concepts

Understanding Statistics

Statistics is a branch of mathematics that involves collecting, analyzing, and interpreting data. It helps us make sense of complex datasets by summarizing and presenting the information in a simple manner.
In the context of this exercise, we deal with test scores, which are quantitative data. The goal is to understand how these scores behave collectively, rather than individually, by identifying measures like the median, which provides insight into the dataset's central tendency.
Central tendency refers to the middle point of data distribution, often measured using the mean, median, or mode. These measures help us understand where most data points cluster and identify any outliers. The median, specifically, is less affected by outliers compared to the mean, which makes it a valuable statistic for understanding the typical score when the dataset includes extreme values.

The Process of Data Analysis

Data analysis involves systematically applying statistical techniques to describe and evaluate data, which allows us to draw meaningful conclusions. In this exercise, Mr. Yunker's test scores are analyzed to find the median.

• Organizing Data: The first step is to arrange the scores in numerical order, which simplifies the process of finding the median and ensures accuracy.
• Identifying the Middle Value: For a list with an odd number of values, the median is the exact middle value. However, with an even number of values, as seen here, the median is the average of the two middle numbers.
• Calculating the Median: With ten scores, calculate the average of the 5th and 6th values to find the median. Even though the numbers are close, taking the precise average, 95.5, provides a clearer picture of where the center of the data is locationally.

Data analysis helps in extracting useful information and making informed decisions based on the results.

Mathematics Education and Median

Teaching concepts like the median is crucial in mathematics education because it develops critical thinking and problem-solving skills. Understanding the median requires students to engage in activities such as sorting and calculating, which are essential skills in mathematics.

Using real-life examples, such as Mr. Yunker's test scores, makes learning more relatable and engaging for students. This exercise not only illustrates the calculation of the median but also emphasizes how such statistical measures can be used to interpret real-world situations.

Throughout mathematics education, encouraging students to work through these processes helps them build a strong foundation in statistics. Mastering concepts such as the median prepares them for more complex data analysis tasks in the future, promoting a deeper understanding of mathematics as both a science and an art.