Exit Velocity The following data represent the exit velocity (in miles per hour) for a simple random sample of 50 homeruns hit during the 2018 Major League Baseball season. With a first class having a lower class limit of 90 and a class width of 4:

e. Does one distribution provide a better summary of the data than the other? Explain.

Verified step by step guidance

1. Step 1: Understand the data and the question. The data consists of 50 exit velocity values (in mph) for home runs, and the question asks whether one distribution provides a better summary of the data than the other. This implies comparing two types of distributions, likely a frequency distribution (grouped data) versus a raw data distribution (ungrouped data).
2. Step 2: Construct a frequency distribution using the given class width and lower class limit. The first class starts at 90 mph with a width of 4 mph, so the classes will be 90-93.9, 94-97.9, 98-101.9, and so on. Count how many data points fall into each class to create the frequency table.
3. Step 3: Calculate summary statistics for both the grouped data (frequency distribution) and the raw data. For the raw data, calculate measures such as mean, median, and standard deviation directly from the 50 values. For the grouped data, estimate these statistics using class midpoints and frequencies.
4. Step 4: Compare the two distributions by analyzing the summary statistics and the shape of the distributions (e.g., histograms or frequency polygons). Consider which method better captures the variability and central tendency of the data.
5. Step 5: Conclude which distribution provides a better summary by discussing the trade-offs: the raw data distribution is more precise but harder to visualize, while the grouped frequency distribution simplifies the data and may reveal patterns more clearly but at the cost of some detail.

Key Concepts

Frequency Distribution and Class Intervals

A frequency distribution organizes data into classes or intervals, showing how many data points fall into each range. Class intervals have a lower limit and a width, which helps group continuous data like exit velocities. This summarization simplifies large datasets and reveals patterns such as data concentration or spread.

Measures of Central Tendency and Spread

Central tendency measures like mean and median summarize the typical value in a dataset, while measures of spread such as range and standard deviation describe data variability. Comparing distributions often involves assessing these statistics to determine which summary better represents the data's overall behavior.

Graphical Representation of Data Distributions

Visual tools like histograms or frequency polygons display data distributions, making it easier to compare shapes, centers, and spreads. A well-chosen graph can highlight differences between distributions and help decide which summary provides a clearer understanding of the data.