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A web site rated 100 colleges and ranked the colleges from 1 to 100 , with a rank of 1 being the best. Each college was ranked, and there were no ties. If the ranks were displayed in a histogram, what would be the shape of the histogram: skewed, uniform, mound-shaped?

Short Answer

Expert verified
The histogram shape would be uniform.

Step by step solution

01

Understand the Histogram

A histogram represents the frequency distribution of data. Each bar in the histogram corresponds to the frequency of observations within each interval or bin. The height of the bar represents how many observations fall into that range.
02

Define the Data Set

In this case, we have the ranks of 100 colleges, ranked from 1 to 100 with no ties, where 1 represents the top-ranked college and 100 the bottom. The data set consists of integers from 1 to 100, each occurring exactly once.
03

Consider Histogram Shape

Since every rank from 1 to 100 is represented exactly once, each number (each rank) occurs exactly once. Therefore, when displayed in bins of individual numbers, each bin will have the same height, representing the number "1" for each rank.
04

Identify Histogram Shape

The histogram, under these conditions, would show bars of equal height across all ranks from 1 to 100 if each rank number forms its own bin. This results in a consistent, flat distribution across all ranks.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency Distribution
A frequency distribution is a straightforward way of organizing and summarizing data. In essence, it shows you how often each value in a set of data occurs. When depicting frequency distribution, particularly through a histogram, you break the data into intervals, known as "bins," and count how many data points fall into each bin. For the colleges ranked from 1 to 100, each rank number falls into its own bin in a histogram. The heights of these bins represent the frequency of each rank, which, in this case, is "1" since each rank appears exactly once. This concept is critical when you're trying to visualize or interpret data because it helps you understand patterns or trends within the data set.
Data Visualization
The way we visualize data profoundly impacts our understanding of it. Data visualization refers to the graphical representation of information and data. By using visual elements like charts, graphs, and maps, data visualization tools provide an accessible way to see and understand trends, outliers, and patterns in data. Histograms are a common choice for visualizing frequency distributions, especially when you want to see how data points are spread across intervals. With a histogram, the frequency and distribution of data can be quickly assessed. For the 100 ranks of colleges, a histogram can effortlessly showcase the uniformity of the data. With each rank appearing once, a histogram visualizes this equal distribution as bars of equal height, providing a clear and immediate way to comprehend the data’s uniform distribution.
Uniform Distribution
Uniform distribution describes a situation where all outcomes are equally likely. When you visualize a uniform distribution on a histogram, it appears as bars of equal height. In the case of the ranks from 1 to 100, each rank is represented once. Therefore, when plotting this on a histogram with each rank number as its own bin, each bin holds precisely one occurrence—the same as every other bin. This results in a flat histogram, where all bars maintain the same height across the entire range. It's an example of a perfectly uniform distribution. In contexts like rankings or scores where data points are evenly distributed, recognizing and creating a uniform distribution visualization can significantly help in quickly perceiving data consistency and balance.

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Most popular questions from this chapter

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