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# Applied Technical Statistics TMTH 3360

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This 5 page Class Notes was uploaded by Erling Dietrich on Saturday September 19, 2015. The Class Notes belongs to TMTH 3360 at University of Houston taught by Staff in Fall. Since its upload, it has received 50 views. For similar materials see /class/208259/tmth-3360-university-of-houston in Mathematics (M) at University of Houston.

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Date Created: 09/19/15

TMTH 3360 NOTES ON COMMON GRAPHS AND CHARTS To Describe Data consider 0 Symmetry o Skewness o Unimodal or bimodal or uniform 0 Extreme values 0 Range of Values and midRange 0 Most frequently occurring values In interpreting graphs consider 0 Horizontal and vertical scales 0 The center point of particular importance in comparing two histograms o The starting point of the vertical scale does it start at 0 How could this affect the interpretation of the data Pareto Diagram 0 Pareto diagrams are special bar chart that are usually used for qualitative data Vertical axis frequency Horizontal axis particular type problem classi cation Bars placed left to right in decreasing order of importance Color Preference of Customers 12 omnm Red Blue Yellow Green Color Goodson 3360gr Data The charts that follow use the following data which is time in minutes Time 110 115 115 120 120 120 120 125 125 125 130 130 130 130 130 135 135 135 140 140 140 140 145 145 150 Dot plots Dot plots are used for quantitative data Each observation is represented as a dot and placed over its number value on a number line Dotplot Time to Complete Task Goodson 3360gr Constructing Frequency Distributions and Histograms Determine the number of classes usually you will have from 5 to 20 it depends on how many data values you have and the spread of the data Determine the class width Generally divide the difference between the largest and smallest values by the number of classes desired round up All the classes should be of equal width to make uniform comparisons ofthe class frequencies 0 Write the class boundaries The lowest class end point must be less than or equal to the smallest data value note that it does not have to equal the lowest value The uppermost class endpoint must be greater than the largest data value 0 Construct a table that includes each class and the corresponding frequencies or relative frequencies Table 1 Frequency Distribution of Time Note Tablel There are 8 classes The class width is 5 The frequency ofthe rst class is l ie there is 1 value Within the class which has a midpoint at 110 This distribution was constructed using Minitab If you are using XL the format is different Examine the histogram for Table 1 It is formulated by plotting the class boundaries on the horizontal axis and bars with heights that correspond to the frequency or relative frequency for each class Frequency I I I I I I MO 115 I20 I25 130 135 140 145 150 Time Goodson 3360gr 3 Constructing Stern and Leaf Plots Create the stem 0 Divide the range of the data into equal units to be used as the stem 0 The rst few digits in each number will be the stem 0 Your data should result in ve to fifteen stems depending on the value of the data 0 List the stem values in order in a vertical column 0 Draw a vertical line to the right ofthe stem values the leaves will be placed to the right of this line Attach the leaves 0 Digits to the right ofthe stem form the leaves 0 Speci cally use the digit to the right of the stem and drop the rest of the digits 0 The leaves are ordered numerically on each branch 0 lfthe number ofleaves in each stem row is too large divide the stems into two groups the rst corresponding to leaves beginning with 0 through 4 and the second with 5 through 9 Advantages 0 Easy to construct 0 Can find the median and quartiles 0 Can read the numerical values from the graph Note it can be dif cult to construct stem and leaf plots if the are many values andor many digits StemandIeaf of Time N 25 Leaf Unit 110 1155 120 12555 130 13555 140 1455 150 Goodson 3360gr 4 Constructing a Box Plot Note more details are on the box plot handout 1 Draw a number line showing the range of values ofyour data Above the number line locate the median and the lower and upper quartiles The difference between the upper and lower quartiles is called the inter quartile range IQR 3 The box extends overthe number line from the lowerto upper quartile ie the sides of the box are on lines through each of the quartile points A line is drawn through the median within the box Draw lines extending to the left and to the right of the box ending at the smallest data point 3 Q25 l5QR the largest data point 5 Q25 l5QR 6 Plot extreme points as individual points I 01h Advantages of the Box plot 0 The graph provides a summary display 0 There is no clutter o It highlights the important features median quartiles and extreme values 0 Additional data does not complicate the graph Interpreting Box plots 0 The box encloses the middle 50 ofthe data 0 lfthe data is symmetrical the median will lay half way between the extreme values 0 lfthe median is close to the left quartile and far from the right extreme the data is skewed right 0 lfthe median is close to the right quartile and far from the left extreme the data is skewed right 0 Two or more Box plots drawn on the same scale and side by side provide an effective way of comparing samples Boxplot of Time 150 140 130 Time 120 MO Goodson 3360gr 5

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