Statistics: Histograms and Frequency Tables
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Questions and Answers

Which of the following is a pictorial method for representing frequency data?

  • Histogram (correct)
  • Dotplot
  • Piechart
  • Barchart
  • Data represented in a histogram can be non-measurable.

    False

    What is the range of the mileages recorded for a sample of hired vehicles?

    81 miles

    The frequency density is calculated by dividing frequency by _____?

    <p>class width</p> Signup and view all the answers

    How many intervals of 10 miles width were deemed sensible for the mileages?

    <p>9</p> Signup and view all the answers

    What is the class interval for vehicles that traveled between 140 and 150 miles?

    <p>140 &amp; &lt; 150</p> Signup and view all the answers

    If the width of a histogram is doubled, then the height for the same frequency must be _____?

    <p>halved</p> Signup and view all the answers

    Match the following types of data presentations with their descriptions:

    <p>Histogram = Pictorial representation of frequency data Barchart = Vertical bars representing categories Piechart = Circular chart divided into sectors Dotplot = Displays individual data points using dots</p> Signup and view all the answers

    Study Notes

    Histograms

    • A pictorial method for representing frequency data; similar to a barchart.
    • Data is measurable (e.g., lengths) not categorical (e.g., colors).
    • Area of the bar in the histogram is proportional to the frequency.

    Frequency Distribution Table

    • A table containing grouped data, providing a clearer picture than individual data values.
    • Used in the construction of histograms, barcharts, pie charts, dotplots, stem-and-leaf plots, and boxplots.

    Constructing a Frequency Distribution Table

    • Step 1: Find the range of the data.
    • Step 2: Determine class intervals, initially all of the same width.
    • Step 3: Construct a frequency distribution table.
    • Step 4: For scarce data at extremes, combine classes.
    • Step 5: If central frequencies are too high, split classes.
    • Step 6: If class intervals are not equal, calculate frequency densities.

    Frequency Densities

    • Frequency density = frequency / class width

    Drawing a Histogram

    • Step 1: Close any open intervals with sensible limits.
    • Step 2: Label both the horizontal and vertical axes, usually frequency or frequency density appears on the vertical axis.
    • Step 3: The horizontal axis represents the values at the interval centers for discrete data, and at the interval boundaries for continuous data.
    • Step 4: The areas of the bars are proportional to the frequency. For example, doubling the width of a bar would require halving its height to maintain the same frequency.
    • Step 5: For discrete data the horizontal axis shows the values at the interval center, and for continuous data, the horizontal axis represents the interval boundaries.

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    Description

    This quiz covers the concepts of histograms and frequency distribution tables in statistics. You will learn how to construct a frequency distribution table and draw histograms based on the data. Additionally, it emphasizes measuring data and understanding frequency densities.

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