College of San Mateo **We aren't endorsed by this school
Aug 20, 2023
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This chapter explores data analysis in the form of graphical displays (dotplots, stem-leaf plots, box-plots, histograms), center, spread, identifying unusual observations and summarizing data (with added emphasis on explaining the message the appears to convey). We are going to learn how to summarize and describe the distribution of data using graphs. 1. Dotplot displays the data of a sample by representing each data with a dot positioned along a horizontal scale, and the frequency on the vertical scale. This display is a convenient technique to use as you first begin to analyze the data. Use dotplot to display the following data set: 4.4, 4.7, 4.7, 7.7, 5.1, 5.1, 5.1, 5.1, 5.1. 2. The Stem-and-leaf display is a combination of a graphical technique and a sorting technique in statistics, and it is well suited to computer applications. Use stem-and-leaf display to summarize the following data set: 10,10, 11, 12, 14, 14, 15, 20, 21, 21, 21, 22, 25, 30, 30, 34. 3. Pie chart and bar chart are graphs that are used to summarize qualitative data. What not to get for mothers on Mother's Day! A recent study among mothers in USA shows that mothers prefer not to receive certain items as gifts on Mother's Day as show below: Teddy bears Chocolate Jewelry Wireless earbuds 45 30 25 50
4. The scatter plot is an appropriate display of bivariate data when both variables are quantitative. Bivariate data refers to the values of two different variables that are obtained from the same population. 5. A histogram is used to summarize continuous quantitative data. All graphic representations of sets of data need to be completely self-explanatory. That includes a descriptive meaningful title, and identification of the vertical and horizontal scales. How to summarize your data using numerical values. We are going to learn how to compute and interpret mean (average), kth % trimmed mean, median, midrange, and mode. These measures of central location are used to define, in some sense, the center of a set of measurements. The average is the typical, or mean, value in the distribution. The symbol for the sample mean is 𝑥𝑥̅ and 𝜇𝜇 (Greek letter mu) for a population mean. The mathematical formula in calculating the sample mean is ∑ 𝑥𝑥 𝑛𝑛 1 𝑛𝑛 . The mean is the average that is the balance point in a distribution. The mean is pulled toward extreme values in an unbalenced distribution (i.e., a right skewed or left skewed distribution). The median is the "centermost" data value in the distribution when the data are arranged from lowest to highest. To find the median data value, make sure you rearrange the data from smallest to largest or from largest to smallest first. If there is an odd number of data values, find the middle data value. If there is an even number of data values, find the middle two data values. Data: 1, 2, 3, 4, and 5. Data: 1, 2, 3, 4, 5, 6. Data: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Data: 1, 2, 3, 4, and 10.
Midrange = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠 𝑣𝑣𝑠𝑠𝑠𝑠𝑣𝑣𝑠𝑠 + 𝑠𝑠𝑠𝑠𝑙𝑙𝑙𝑙𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠 𝑣𝑣𝑠𝑠𝑠𝑠𝑣𝑣𝑠𝑠 2 The 10% trimmed mean is computed by removing the largest 10% of values and the smallest 10% of values from the data set and then computing the mean of the remaining middle 80% of values. How do we determine the total amount of property taxes for the city if we know the number of properties, the mean dollar value of all properties, and the tax rate? The mode is used to describe the most frequent observed data in the distribution. No special computation is involved in finding the mode. A simple inspection of the frequency of occurrence of each data value is all that is required. Remember: Mode is not a frequency, but rather the value that occurs most often. For example: In the set of scores below, 73, 73, 73, 75, 78, 79, 82, 82, 85, 88, 89, 95, 95, 98 the mode is 73.
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