Ch 3.3 SAYOxlsx

s Complete with 2.2 Not =COUNTIF(x,@y) Steps to Creating Bins =SUM(x,y) 1 calculate the range =@x/@y 2 divide range by # of bins wa 3 4 find lower and upper limits for e 5 use Data analysis tool to make h Steps to making a histogram in EXCEL 1 Click Data Tab, Data Analysis, Choo 2 Highlight data for Input Ra 3 Use Upper limits for bin range with 4 Click on cell you want the histogram fo How to Find Cumulative Frequency number in given bin plus all smaller bin Complete with 3.1 Not How to do when given a frequency tabl Mean =average Median =median Mode =MODE.MULT Measures of Center and shapes of distributio symetrical mean, median, and mode are roug left Skewed mean is smaller than med right skewed mean is larger than the me round up to the next whole n e total row, Click insert Tab, Choose ce on worksheet, Move chart to ls, Rename Chart Title and Both Axis equencies, Include column headings ose top left choice , Move chart to ename Chart Title

1.1 Vocabulary word Definition Statistics Individual Population Sample Parameter Statistic Qualitative Variable Quantitative Variable Discrete data Continuous data Nominal Ordinal Is the Study of how to collect, organize, analyze, and interpret data collected froma a group A person or object that you are interested in finding out information about. Set of all values of the variable for the entire group of individuals A subset from the population. It looks just like the population. But contains less data A number calculated from the population. Usually denoted with a greek letter. This number is a fixed, unkown number that you want to find. A number calculated from the sample. Usually denoted with letters from the Latin alphabet, though sometimes there is a Greek letter with a ^(called a hat) above it. Since you can find smaples, it is readily known, though it changes depending on the sample taken. It is used to estimate the parameter value. Answer is a word or name that describes a quality of the individual Answer is a number, something that can be counted or measured from the individual data can only take on particular values like integers. Discrete data are usually things you count Data that can take on any value. Usually things you measure. Date is just a name or category. There is no order to any data and since there are no number, you cannot do any arethmetic on this level of data. date is nominal, but you can now put that data in order, since one value is more or less than another value. You cannot do arithmetic on this data, but you can now put data values in order

Temperature and time on a clock height, weight, distance, and time Example from Book Obtain a list of patients who had surgery at Banner Health facilities. Number these patients, and then use a random number table to obtain the sample Obtain a list of patients who had surgery at all Banner Health facilities. Divide the patients according to type of surgery. Draw simple random samples from each group. At the beginning of the year, instruct each banner Health facility to record any complications from every 100th surgery. Randomly select some Banner Health facilites from each of the seven states, and then include all the patients on the surgery lists of the states Instruct each Banner Health Facilities to record any complications from 20 surgeries this week and send in the results Banner Health is a several state nonprofit chain of hospitals. Management wants to assess the incident of complications after surgery.

Sampling error: Non-sampling error hidden bias Non-response error Voluntary response error this is the difference between the sample results and the true population results. this is where the sample is collected poorly either through a biased sample or through error in measurements. is where the question are asked in a way that makes a person respond a certain way. Can also be called a loaded question is where you send out a survey but not everyone returns the survey is where people are asked to respond via phone, email or online.

if you take sample of 5 peoples height in your class, you will get 5 numbers. If you take another sample of 5 people heights in your calls, you will likely get 5 different numbers. suppose you find that a new drug for high blood pressure does reduce the blood pressure of patients. When you look at the improvement it actually doesn’t amount to a large difference. Even though statistically there is a change, it may not be worth taking marketing the product because it really isn't that big of a change. a poll was done where people were asked if theory believe that there should be an amendment to the constitution protecting a woman's right to choose. About 75% of all people question said yes. Another poll was done where people were asked if they believe that there should be an amendment to the constitution protecting the life of an unborn child. about 60% for all people question said yes. these two question deal with the same issue, though giving opposite results but how the question was asked affected the outcome. physical mailing are the least desirable way to conduct survey Suppose the telephone poll is conducted by contacting U.S. citizens via landlines about their view of gay marriage. Suppose over 50% of those called do not support gay marriage. Does that mean that you can say over 50% of all people in the U.S. do no support gay marriage?

Statistics class drive. , Nissan, Chevy, Toyota, san, Mercedes, Chevy, Ford, ssan, Honda, Porsche, Ford, Nissan, Toyota, Chevy, ssan, Honda, Toyota, Toyota,

nd calculations Put Bar Graph of Frequency in this box. calculations. e e 24.0% 10.0% 20.0% 12.0% 24.0% 10.0% 100.0% Graph equencies DO NOT include total row ph Put Bar Graph of Relative Frequency in this box. e place on worksheet s Title and Data Labels oth Axis Titles raph EQUENCY FOR PIE GRAPHS equencies DO NOT include total row ph e place on worksheet s Put pie Graph of Relative Frequency in this box. Relative Frequency Toyota Ford Chevy Honda Nissan 0 2 4 6 8 10 12 14 12 5 10 6 12 Car types driven by stats students Car type frequency Toyota Ford Chevy Honda Nissan 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 24.0% 10.0% 20.0% 12.0% 24.0% Car types driven by stats student Car type Relative frequency car types driven by stats students

24% 10% 20% 12% 24% 10% Toyota Ford Chevy Honda Nissan Other

n Other 5 Other 10.0%

Types of graphs that represent quantitative data Sick Days taken in 4.5 Histogram 6.5 14 6 6 5 Histogram Vocabulary 13 Bin/class Bar of a histogram 17 Range Largest data value- smallest data value 9 class width how wide is each bar 7 upper limit largest possible number in a given bar 5.5 lower limit smallest possible number in a given bar 3.5 6 Steps to Creating Bins 7 1 calculate the range 7 2 divide range by # of bins wanted 6 3 3 4 find lower and upper limits for each class 7.5 5 use Data analysis tool to make histogram 4.5 6.5 Difference between frequency and relative frequency Histograms 4 Frequency counts # in each bin 6 realative frequency shows percentage in each bin 6 5 Cumulative Frequency Distribution Tables 13 number in given bin plus all smaller bins 7 9 Shapes of Histograms 7 symmetrical 5.5 Right skewed highest frequency on left with tail on right 13.5 left skewed highest frequency on right with tail on left 6 7 7 6 3 7.5 symmetrical or bell shaped round up to the next whole number highest frequency in the middle both sides relatively equally shaped

Left skewed data right skewed

n 1 year Largest max 17 smallest min 3 range max-min 14 bins 5 lower limit for 1st bin is always minim divide 2.8 round 3 = class width Bin # lower upper Frequency Relative Freq Cumulative Frequency 1 3 6 10 27.8% 10 2 6 9 19 52.8% 29 3 9 12 2 5.6% 31 4 12 15 4 11.1% 35 5 15 18 1 2.8% 36 Total Freq 36 100.0% Create Histogram: Click Data Tab, Data Analysis, Choose Histogram Highlight data for Input Range Use Upper limits for bin range without header Click on cell you want the histogram for Output Range Bin Frequency 6 10 9 19 12 2 15 4 18 1 More 0 6 9 12 15 18 More 0 5 10 15 20 10 19 2 4 1 0 Sick days taken in one year Upper limit of Hours taken Frequency

mum. Frequency

Define = Measures of Center way to find the middle of the data- average- Mean Median 3 types of Measures of Center Mode mode the data number happens most often mean add up all the data number and fivide by the total frequency median after startingthe data in order then find middle number Data Set 1 4 3 types of Modes 6 unimodal only 1 mode- 1 number happens most frequently 6.5 bimodal 2 numbers share the highest frequency 7 no mode more than 2 share highest frequency 8 8 8 Comments about modes 8 very large are smll numbers will no affect the mode 8.5 9 10 Comments about Means very large or small numbers will change the mean a lot 7.5 Mean 7.5 Median 8 Comments about Medians Mode 8 very large or small numers will change the median only slightly if any Data Set 1 Data Set 2 Mean 7.5 Mean 14.53846 Standard E 0.537484 Standard E 7.133674 Median 8 Median 8 Mode 8 Mode 8 Standard D 1.699673 Standard D 25.72083 Sample Var 2.888889 Sample Var661.5609 Kurtosis 0.930288 Kurtosis 12.89031 Skewness -0.763721 Skewness 3.584184 Range 6 Range 96 Minimum 4 Minimum 4 Maximum 10 Maximum 100 Sum 75 Sum 189 Count 10 Count 13 AN To find the m go to data analysis for input ra for output range c check s

Measures of Center and shapes of dist =AVERAGE( symetrical mean, median, and mode ar =MEDIAN( left Skewed mean is smaller tha =MODE.MULT( right skewed mean is larger than t Data Set 2 4 8 7 9 6 6.5 8 10 8.5 8 100 7 7 14.538462 8 8 7 16 Finding the mean of a frequenc 16 multiply x value by frequen 16 divide total of X*F by total freq 17 X = age F = frequency X*F 17 16 3 48 17 17 4 68 17 18 1 18 18 19 4 76 19 20 6 120 19 21 3 63 19 22 7 154 19 23 2 46 24 2 48 25 1 25 26 2 52 27 1 27 28 2 56 29 4 116 30 0 0 31 0 0 32 0 0 NOTHER WAY mean, median and mode: s, choose descriptive statistics ange highlight your data choose cell you want info put summary statistics

33 1 33 sum 43 950 total frequency total of all ages mean 22.09302

tribution graphs re roughly the same Mode is always highe an median the median cy table ncy quency Process Mean 22.0930 columns the Median 22 total freque Mode 22 Shape symmetrical 21.5 21 x 21 22nd number is my m

est point on graph because it has the highest frequency How to en sum of multiplied numbers and divide it by total f ency/ 2 find the x value in the answer order number X value with the highest frequency mean , median, mode are the same 22nd number in order 22nd numer is 22 middle number

Measures of Spread shows if the data is spread apart or close together 3 types of Measures of Spread range distance from largest to the smallest data number standard deviation the average distance a data value is from the mean IQR learn in section 3.3 Properties of Range add in a very large or very small number to the data, the range will change a lot Properties of Standard Deviation Adding in a very large or small numbers will only change the standard deviation moderately Define Z Score how many standard deviations away from the mean a number is Formula for Z Score When is a number considered to be unusual? any z score that is greater than 2 or less than -2 Properties of Z Score if Z score is positive, then the data number is greater or above the mean if Z score is negative, then the data number is smaller or below the mean z=(x-mean)/ st. DEV

Data Set 1 10 20 30 40 50 DATA SET 1 Data Set 2 10 29 30 31 50 Mean 30 Data Set 3 Standard Error 7.071068 28 29 30 31 32 Median 30 Mode #N/A Standard Deviation 15.81139 Range St. Dev. Z score of 20 Sample Variance 250 Data Set 1 Kurtosis -1.2 Data Set 2 Skewness 0 Data Set 3 Range 40 Minimum 10 Maximum 50 Data Set 1 standard deviation = 15.8113883 Sum 150 Data # 10 20 30 40 50 Count 5 Z score -1.2649 -0.632456 0 0.6325 1.2649 DATA SET 3 z score 70 2.5298 is unusual z score 0 -1.897367 not unusual Mean 30 30+15.81139 45.81 Z= 1 Standard Error 0.707107 Median 30 30- 15.81139 14.18861 Z= -1 Mode #N/A Standard Deviation 1.581139 10 is 1.2649 standard deviations below the mean Sample Variance 2.5 20 is 0.6325 standard deviations below the mean Kurtosis -1.2 30 is no standard deviation away from the mean Skewness 0 40 is 0.6325 standard deviations above the mean Range 4 50 is 1.2649 standard deviations above the mean Minimum 28 Maximum 32 Sum 150 given the Z score, find the X value Count 5 Data set 1 what data number is 2 standard deviations below the mean Z=-2 X=? z=(x-mean)/ st. DEV Z*ST. DEV = X - mean Z*ST. DEV+mean = X X= Z*ST. DEV +MEAN x= -1.6228 mean 30 - st deviation 14.18861 - st deviation -1.622777

DATA SET 2 Mean 30 Standard Error 6.332456 Median 30 Mode #N/A Standard Deviation 14.1598 Sample Variance 200.5 Kurtosis 1.950249 Skewness 0 Range 40 Minimum 10 Maximum 50 Sum 150 Count 5

RANKING Percentile what percent did lower than a data number= breaks data into 100 pieces. Quartile all data and break it into 4 equal pieces. Each quarile represents 25% What you get when you divide your data into quartiles Min smallest data value Q1 25% lower and 75% higher median 50% lower and 50% higher Q3 75% lower and 25% higher Max highest data value 5 - Number Summary Min =MIN(data range) Q1 =percentile.exc(data range,.25) median =median(data range) Q3 =percentile.exc(data range,.75) Max =max(data range) IQR - Interquartile Range how wide is it between Q1 and Q3 IQR =Q3-Q1 Box and Whiskers Plot graph of the 5 number summary Stacked Box and Whiskers Plots

lower fence upper fence lower fence upper fence min Q1 med Q3 Max IQR Lower Fence Upper Fence right skewed because graph is pulled more to the right 25% min 3 This chart isn't available in your version of E Editing this shape or saving this workbook i permanently break the chart.

Fences Definitions calculates the cutoff for unusually low numbers, anythign lower than the lower fence is unusual calculates the cutoff for unusually high numbers, anythign higherthan the upper fence is unusual Fences Formula =Q1- (IQR*1.5) = Q3+(IQR*1.5) Life Expectancy of Southeast Asian Countries in 2011 64 65 69 74 77 9 51.5 87.5 between q1 and q3 middle 50% 25% 25% 25% max 17 Q1 Q3 5.5 median 7.735 6.35 Min 3 Q1 5.5 median 6.25 Q3 7.375 Max 17 IQR 1.875 LF 2.6875 UF 10.1875 Excel. into a different file format will

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