Math 1040, Chapter 2
Math 1040, Chapter 2 MATH 1040
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This 4 page Class Notes was uploaded by Linda Davila on Tuesday January 26, 2016. The Class Notes belongs to MATH 1040 at Southern Utah University taught by Derek Hein in Winter 2016. Since its upload, it has received 21 views. For similar materials see Statistics in Mathematics (M) at Southern Utah University.
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Date Created: 01/26/16
Math 1040 Statistics Chapter Two Section 2.1 o Distribution A way to describe the structure of a particular data set or population o Frequencies (f) The number of data values in a category of a frequency distribution o Frequency distribution a display of the values that occur in a data set and how often each value, or range of values, occurs. o Class a category of data in a frequency distribution. o Class Width the difference between the lower limits or upper limits of two consecutive values. o Lower Class Limit the smallest number that can belong to a particular class. o Upper Class Limit the largest number that can belong to a particular class. o Class Boundary A class boundary is the value that lies half way between the upper limit of one class and the lower limit of the next class. After finding one boundary, add (or subtract) the class width to find the net class boundary. The boundaries of a class are typically given in interval form: lower boundary upper boundary o Class Midpoint Class midpoint = lower limit + upper limit 2 o Relative Frequency The relative frequency is the fraction or percentage of the data set that falls into a particular class given by: Relative frequency = f/n o Where f is the class frequency o n= sample size, given by n= ∑ fi o Cumulative Frequency The cumulative frequency is the sum of the frequencies of a given class and all the previous classes. The cumulative frequency of the last class is equal to the sample size Tip: always grows! Section 2.2 Graphic Displays of Data o Quantitative Data Shows how large each category is in relation to a whole. Can only display qualitative data. To find the degree, divide f/n to get a decimal Pie than multiply that by 360 to get the degree. Graph Graphs that use bars, instead of parts of a circle, to represent the amount of data in each category. Can be used for qualitative data, without restrictions on what types Bar of qualitative data you must have. Graph A bar graph with the bars in descending order of frequency. Typically used with nominal data. Pareto Graph A bar graph that compares the same categories for different group. Side by Side Bar A bar graph that compares the same categories for different groups and shows category totals. Sta cked Bar Chart o Qualitative Data A bar graph of a frequency distribution of quantitative data; horizontal axis is a number line. Midpoints Histo Class boundaries gram Visual display of the frequency of each class of quantitative data that uses straight lines to connect points plotted above the class midpoints. Class boundaries Fre *Needs anchors quency Polygon Displays the cumulative frequency of each class of quantitative data by using straight lines to connect points plotted above the class boundaries. *One anchor Ogiv e Stem and Leaf Plot Retains the original data; the leaves Ste Lea are the last significant digit in each m f data value and the stems are the 0 2,4, remaining digits. 4 1 1,4, 5 2 6 3 1,1 4 4,5, 9 Dot Plot A dot plots retains the original data by plotting a dot above each data value on a number line. 1 2 3 4 5 6 7 8 9 10 Uses straight lines to connect points plotted at the value of each measurement above the time it was taken. Lin e Graph Steps to build a frequency polygon: Mark the class boundaries on the xaxis and the frequencies on the yaxis. Add the midpoints to the xaxis and plot a point at the frequency of each class. Connect the dots. Constructing a stem and leaf plot Create two columns; left= stem and right= leaf List each stem that occurs in the data set in numerical order List each leaf next to its stem Create a key o Ex. 12|3 = 123 Section 2.3 Analyzing Graphs o Shapes of graphs Basic shapes of distribution: Uniform Symmetrical, but not uniform Skewed to the right Skewed to the left o Appropriateness of the graph Time series graph is a line graph that is used to display a variable whose values change over time. Cross sectional graph displays information collected at only one point in time.
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