Organizing and Summarizing Data
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| What is a frequency Distribution? | A frequency distribution lists each category or value of a variable and the frequency of occurrences and/or relative frequency of occurrences for each category or value.
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| What is Relative Frequency? | The proportion (or percent) of observations within a category and is found by using the formula: Frequency/(sum of all frequencies)
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| What is a Pareto Chart? | A bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
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| How is a histogram constructed? | A histogram is constructed by drawing rectangles for each class of data whose height is the frequency or relative frequency of the class. The width of each rectangle should be the same and they should touch each other.
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| How is a Stem-and-Leaf Plot constructed? | The stem of a data value will consist of the digits to the left of the right-most digit -- separated by a vertical bar. The leaf of a data value will be the right-most digit. For example, a data value of 154 would have 15 as the stem and 4 as the leaf.
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| How is a time-series plot constructed? | A time-series plot is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable on the vertical axis. Line segments are drawn connecting the points.
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| Suppose you surveyed 100 people to determine their preferred color for an automobile. Would it be appropriate to use a bar chart or histogram to organize the data? Why? | It is appropriate to use a Bar chart to organize the data because the variable used (preferred colors of automobiles) is qualitative.
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| Jim collected data on the heights of 200 children entering the first-grade in Clayton County, Georgia. If Jim wants to organize the data, would it be appropriate to use a bar chart of histogram? Why? | It is appropriate to use a histogram to organize the data because the variable used (height of children entering the first-grade in Clayton County, Georgia) is quantitative.
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| Sue collects data on the waiting time before customers are seated in a busy restaurant near her office. She uses time intervals in minutes to construct a grouped frequency table. Why is a grouped frequency chart appropriate? | A grouped frequency chart is appropriate because the variable (waiting time) is continuous. Therefore, you cannot count frequency for individual values of time; but rather time intervals are required.
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| In constructing Grouped Frequency charts, what do we mean by “classes”? | Categories of data are created for continuous data using intervals of numbers called classes.
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| What do we mean by “class limits”? | Class limits are the smallest value for a particular class (lower class limit) and the largest value for a particular class (upper class limit).
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| How is the “class width” determined? | The class width is the difference between consecutive lower class limits. For example, if two consecutive classes are: 10 – 19 and 20 – 29, the class width would be 20 – 10 = 10.
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| After a frequency distribution chart is created, it is easy to construct a histogram. How is the histogram useful? | The histogram is useful in identifying the shape of the data distribution.
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| What are the typical shapes that we might use to describe a frequency distribution based on its histogram? | Five common shapes that are used in classifying or describing frequency distributions are: (1) symmetric; 2) uniform; 3) skewed left; 4) skewed right; and 5) bimodal.
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