Graphing Data Sets
Graphing Data Sets MAT117
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This 5 page Class Notes was uploaded by WB on Thursday October 8, 2015. The Class Notes belongs to MAT117 at Pace University taught by Dr. Glenn Miller in Fall 2015. Since its upload, it has received 21 views. For similar materials see Elementary statistics in Mathematics (M) at Pace University.
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Date Created: 10/08/15
Graphing Data Sets 1 Frequency distribution Two types 1 Grouped with classes 2 Ungrouped no classes a Classes a more efficient way to organize the data counting the number of observations in various intervals of values How to find a class gt 1 Start with a round number below the smallest data value 2 Determine the range of values from the lowest class limit up to highest class limit a round value a little higher than the highest data value 3 Determine how many classes to split the data into Larger sample size more classes more bars in the bar graph 4 NB classes should NOT overlap classes should be of EQUAL width b Relative frequency the percentage of the data that lies in an interval Why it is more useful to the enduser than frequency gt ex If a professor states that 10 students got an A in his class last semester is that good or bad I You need to know how many students were in the class By compared with 10 out of 100 which means 10 of the students got an A 10 out of 20 which means 50 of the students got an A is a better result c Cumulative relative frequencies related to percentiles II Graphs histogram amp ogive Elements of the graph title amp units a Histogram A histogram is similar to a bar graph except that the bars should touch since there should not be gaps between the bars for a continuous data set x axis class boundaries derived from the data yaxis relative frequency Shapes of histogram 1 Bellshaped normal distribution 2 2 a 2 Skewed to the right 2 gt 3 ex Income in the US is skewed to the right A few individuals with extremely high incomes relative to the rest of US skew the distribution away from the normal shape 3 Skewed to the left 2 lt a 4 Bimodal Because of the expectation of getting a bell shape the two bells might mean that there are in fact two populations under consideration and the researcher might have to study them separately EX A study of the heights of college students This study would probably yield a bimodal distribution because one sample cannot adequately represent the two distinct populations male and female college student 5 Uniform b Ogive An ogive is a line graph XaXis class boundaries derived from the data yaXis cumulative relative frequencies Class limits are end numbers of a class interval Class boundaries are true class limits EX a class interval 1 5 1 is called the lower limit LL and 5 is the upper limit UL How to calculate class boundaries EX calculate the class boundaries for the class interval 1 5 Since it is counted by ones 12345 Meaning the unit of measurement is 1 a unit 2 upper class boundary5 155 lower class boundary1 105 so the required class boundaries is 05 55 Ex find the class boundaries for the given class interval 75105 Since it is counted by tenths 010203 etc Meaning the unit of measurement is a tenth 01 2 upper class boundary105 011055 lower class boundary75 01745 so the required class boundaries is 745 1055 Practice For the data below make a GROUPED frequency distribution using 2039 as the first class make a histogram and describe its shape Predict based on the shape of the histogram the relationship between the mean and the median Birth Weight in Pounds of 35 infants 56 60 73 102 36 66 40 42 72 75 117 49 76 76 103 63 60 84 52 59 44 67 59 52 73 75 49 64 74 48 68 27 51 66 37 I Data in order 27 49 60 73 102 36 51 63 73 103 37 52 64 74 117 40 52 66 75 42 56 66 75 44 59 67 76 48 59 68 76 49 60 72 84 Classes Frequency Relative frequency Cumulative relative frequency 0 2 39 3 9 9 4 59 12 34 43 6 79 16 46 89 8 99 1 3 91 10 119 3 9 100 35 Weight of Infants at Birth gt 50 U 5 40 1 5quot 30 39 8 a 20 gt 1 10 39 E g 0 239 459 679 8 99 10119 weight lbs To make an ogive we need to first calculate the class boundaries Lower class boundary2 01195 Upper class b0undary39 01395 195 cumulative relative frequency 395 Weight of Infants at Birth 595 795 995 weight lbs 1195 Median is about 63 lbs
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