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Which of the following is a pictorial method for representing frequency data?
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 _____?
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How many intervals of 10 miles width were deemed sensible for the mileages?
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What is the class interval for vehicles that traveled between 140 and 150 miles?
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If the width of a histogram is doubled, then the height for the same frequency must be _____?
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Match the following types of data presentations with their descriptions:
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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.
