Descriptive statistics

Use statistical software to create, interpret, and analyze two histograms in a Word document.
Introduction
Descriptive statistics are just what they sound like, statistics that allow you to describe or summarize the data with regard to such things as their distribution and their spread. Descriptive statistics provide you with a picture of your data while inferential statistics (which we will discuss in subsequent assessments) allow you to draw conclusions about relationships between variables or differences between groups.
A solid understanding of descriptive statistics is foundational to grasping the concepts presented in inferential statistics. This assessment measures your understanding of key elements of descriptive statistics.
Your first statistical software assessment includes two sections in which you will do the following:
1. Create two histograms.
2. Calculate measures of central tendency and dispersion.

 

Sample Solution

  1. Open the statistical software and import the data set that you want to create histograms for.
  2. Choose the “histogram” option from the statistical software’s menu bar.
  3. In the histogram dialog box, specify the following settings:
    • The variable that you want to create the histogram for.
    • The number of bins (or bars) that you want the histogram to have.
    • The range of values that you want the histogram to display.
  4. Click the “OK” button to create the histogram.
  5. Interpret the histogram by looking at the following features:
    • The shape of the distribution: Is the distribution symmetrical or skewed?
    • The center of the distribution: Where is the highest point of the distribution?
    • The spread of the distribution: How wide is the distribution?
    • Outliers: Are there any values that fall far outside the rest of the distribution?
  6. Analyze the histogram by answering the following questions:
    • What does the shape of the distribution tell you about the data?
    • What does the center of the distribution tell you about the data?
    • What does the spread of the distribution tell you about the data?
    • Are there any outliers? If so, what do they tell you about the data?

Here is an example of how to create, interpret, and analyze two histograms in a Word document using statistical software:

The data set that we will use for this example is the heights of 100 students. The heights are in centimeters.

  1. Open the statistical software and import the data set.
  2. Choose the “histogram” option from the statistical software’s menu bar.
  3. In the histogram dialog box, specify the following settings:
    • The variable that you want to create the histogram for is “Height”.
    • The number of bins (or bars) that you want the histogram to have is 10.
    • The range of values that you want the histogram to display is 150 to 200.
  4. Click the “OK” button to create the histogram.

The following histogram shows the distribution of the heights of the 100 students:

The histogram is symmetrical, with the highest point in the middle. The center of the distribution is around 175 centimeters. The spread of the distribution is from 150 to 200 centimeters. There are no outliers.

We can interpret the histogram as follows:

  • The distribution of the heights is symmetrical, which means that there are an equal number of students who are taller than 175 centimeters and shorter than 175 centimeters.
  • The center of the distribution is around 175 centimeters, which means that the average height of the students is 175 centimeters.
  • The spread of the distribution is from 150 to 200 centimeters, which means that the tallest student is 200 centimeters tall and the shortest student is 150 centimeters tall.
  • There are no outliers, which means that all of the heights fall within the expected range.

We can analyze the histogram by answering the following questions:

  • The shape of the distribution tells us that the heights are evenly distributed.
  • The center of the distribution tells us that the average height is 175 centimeters.
  • The spread of the distribution tells us that the heights range from 150 to 200 centimeters.
  • There are no outliers, which means that all of the heights fall within the expected range.

The histogram is a useful tool for visualizing the distribution of data. It can be used to answer questions about the shape, center, and spread of the distribution. The histogram can also be used to identify outliers.

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