Representing Data Graphically: Learn It 3

Looking at Quantitative Data

To fully grasp the intricacies of statistical analysis, let’s focus on a practical example: examining the age distribution among Oscar winners. This exploration will help us understand how quantitative data is used to interpret real-world scenarios and trends. Consider the statistical question: How old are the winners of the Best Actress and Best Actor awards at the Academy Awards (more commonly known as “the Oscars”)?

Quantitative data are always numbers. Quantitative data are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics are examples of quantitative data. Quantitative data may be either discrete or continuous.

  • All data that are the result of counting numbers are called quantitative discrete data.
  • Data that are not only made up of counting numbers, but that may include fractions, decimals, or irrational numbers, are called quantitative continuous data.

Histograms

Histograms are an excellent tool for visualizing data sets with numerous observations by organizing these observations into uniformly sized bins, which appear as bars. The flexibility to adjust the bin width ensures histograms can effectively display vast amounts of data without becoming cluttered. Each bin includes its left-edge number (the lowest value) but excludes the right-edge number (the highest value), facilitating precise data representation. Additionally, histograms are uniquely designed with contiguous bars, eliminating any gaps between them for a coherent visual interpretation.

histogram

Histograms efficiently illustrate the distribution of numerical data by grouping data into ‘bins’ of equal width, with the height of each bar representing the frequency of data within that range, making it easy to observe patterns such as skewness, peaks, and spread within the data.

Histogram Binwidth

Changes in the binwidth of a histogram can change the appearance of the distribution. But, it’s important that a histogram has an appropriate binwidth, so that it can give you good information about the shape of the distribution.

Create a histogram for the data “Hours Watching TV (2018)” using the Describing and Exploring Quantitative Variables tool below. Steps to create a histogram:

STEP 1: Select “Single Group”

STEP 2: Select the Data Set “Hours Watching TV (2018)”

STEP 3: Under “Choose Type of Plot”, select “Histogram”

STEP 4: Create three histograms with different binwidths “[latex]2[/latex]“, “[latex]5[/latex]“, and “[latex]10[/latex].”


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Evaluating Histograms

Download the data set “Oscars Age” spreadsheet and create a histogram to answer the following questions.


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