Warm-up A study of the size of jury awards in civil cases (such as injury, product liability, and medical malpractice) in Chicago showed that the median.

Warm-upWarm-up

A study of the size of jury awards in civil A study of the size of jury awards in civil cases (such as injury, product liability, and cases (such as injury, product liability, and medical malpractice) in Chicago showed medical malpractice) in Chicago showed that the median award was about $8,000. that the median award was about $8,000. But the mean award was about $69,000. But the mean award was about $69,000. Explain how this great difference between Explain how this great difference between the two measures of center can occur.the two measures of center can occur.

Warm upWarm up

Pg. 77 #R1.9Pg. 77 #R1.9

Ogives and TimeplotsOgives and Timeplots

O-What???O-What???

OgivesOgives

Pronouced Oh-JivesPronouced Oh-Jives

An ogive is a relative cumulative frequency An ogive is a relative cumulative frequency graph.graph.

Oh, that’s crystal clear! Oh, that’s crystal clear!

Frequency TablesFrequency Tables

This data set lists the This data set lists the number of books that number of books that are on the desks of are on the desks of 50 college students at 50 college students at 8:00 a.m. on Monday 8:00 a.m. on Monday morning. Using this morning. Using this data, count how many data, count how many times each value times each value occurs. Make a tally occurs. Make a tally chart.chart.

33 55 1010 44 66

77 22 1212 1111 99

77 55 33 44 88

55 1010 99 1414 77

22 11 00 55 77

88 99 1414 1818 1010

11 66 77 88 55

33 1010 1212 33 44

22 22 66 44 33

55 1010 99 99 66

Frequency and Relative FrequencyFrequency and Relative Frequency

Frequency simply means how many times Frequency simply means how many times a certain value occurs. Your tally marks a certain value occurs. Your tally marks represent the frequency.represent the frequency.

Relative frequency means you convert the Relative frequency means you convert the number of tally marks to a percent of the number of tally marks to a percent of the total. i.e. divide by 50total. i.e. divide by 50

Relative FrequencyRelative Frequency

ValueValue FrequencyFrequency Relative Relative FrequencyFrequency

00 11 1/50 = .02 = 2%1/50 = .02 = 2%

11 22 2/50 = .04 = 4%2/50 = .04 = 4%

22 44 4/50 = .08 = 8%4/50 = .08 = 8%

33 55 5/50 = .10 = 10%5/50 = .10 = 10%

44 44 4/50 = .08 = 8%4/50 = .08 = 8%

Cumulative FrequencyCumulative FrequencyCumulative frequency tells us how many values fall at or below a certain number!Cumulative frequency tells us how many values fall at or below a certain number!

Simply add your tally marks from the lowest value up to calculate cumulative Simply add your tally marks from the lowest value up to calculate cumulative frequency.frequency.

ValueValue FrequencyFrequency Relative Relative FrequencyFrequency

Cumulative Cumulative FrequencyFrequency

00 11 1/50 = .02 = 1/50 = .02 = 2%2%

11

11 22 2/50 = .04 = 2/50 = .04 = 4%4%

33

22 44 4/50 = .08 = 4/50 = .08 = 8%8%

77

33 55 5/50 = .10 = 5/50 = .10 = 10%10%

1212

44 44 4/50 = .08 = 4/50 = .08 = 8%8%

1616

Cumulative Frequency vs. Relative Cumulative Frequency vs. Relative FrequencyFrequency

Cumulative frequency – quantity.Cumulative frequency – quantity.

Relative cumulative frequency is the Relative cumulative frequency is the percentpercent of data that fall at or below a given of data that fall at or below a given value.value.

This is also called a This is also called a PERCENTILEPERCENTILE, which , which is a word you will hear frequently.is a word you will hear frequently.

Relative FrequencyRelative FrequencyValueValue FrequencyFrequency Relative Relative

FrequencyFrequencyCumulative Cumulative FrequencyFrequency

Relative Relative Cumulative Cumulative FrequencyFrequency

00 11 1/50 = .02 = 2%1/50 = .02 = 2% 11 1/50 = .02 = 1/50 = .02 = 2%2%

11 22 2/50 = .04 = 4%2/50 = .04 = 4% 33 3/50 = .06 = 3/50 = .06 = 6%6%

22 44 4/50 = .08 = 8%4/50 = .08 = 8% 77 7/50 = .14 = 7/50 = .14 = 14%14%

33 55 5/50 = .10 = 5/50 = .10 = 10%10%

1212 12/50 = .24 = 12/50 = .24 = 24%24%

44 44 4/50 = .08 = 8%4/50 = .08 = 8% 1616 16/50 = .32 = 16/50 = .32 = 32%32%

Cumulative Frequency Graph

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Relative Cumulative Frequency Graph

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THIS is an ojive!THIS is an ojive!

So what’s the point?So what’s the point?

We are able to tell where an individual in a We are able to tell where an individual in a population stands relative to others.population stands relative to others.

Example… Look at your graph. What Example… Look at your graph. What percent of students have no more than 10 percent of students have no more than 10 books on their desk Monday morning?books on their desk Monday morning?

Relative Cumulative Frequency Graph

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About 88%.

How many books do 40% of the students have on How many books do 40% of the students have on their desks Monday morning?their desks Monday morning?

Relative Cumulative Frequency Graph

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0 5 10 15 20

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Time PlotsTime Plots

Shows each observation at the time it was Shows each observation at the time it was measured.measured.

The time scale is on the horizontal axis.The time scale is on the horizontal axis.

The variable of interest (temperature, The variable of interest (temperature, stock prices, gasoline prices) is on the stock prices, gasoline prices) is on the vertical axis.vertical axis.

Look for a Look for a trendtrend, or an overall pattern., or an overall pattern.

Section 1.2 Comparing Section 1.2 Comparing DistributionsDistributions

Comparing DistributionsComparing Distributions

Often, the question of interest is which Often, the question of interest is which car/drug/fuel additive etc. is preferable. In car/drug/fuel additive etc. is preferable. In this case, we need to be able to compare this case, we need to be able to compare distributions.distributions.

Graph Choices for Comparing Graph Choices for Comparing DistributionsDistributions

For categorical For categorical variables, a side-variables, a side-by-side bar graph by-side bar graph works well.works well.

Graph Choices for Comparing Graph Choices for Comparing DistributionsDistributions

For two small quantitative data sets, a back-to-For two small quantitative data sets, a back-to-back stem and leaf plot is effective.back stem and leaf plot is effective.

Graph Choices for Comparing Graph Choices for Comparing DistributionsDistributions

Boxplots alone contain little detail, but Boxplots alone contain little detail, but side-by-side boxplots effectively compare side-by-side boxplots effectively compare large sets of quantitative data.large sets of quantitative data.The plot is useful for showing the The plot is useful for showing the comparison of several groups. This comparison of several groups. This example shows a fat absorption test in example shows a fat absorption test in patients who have AIDS, AIDS Related patients who have AIDS, AIDS Related complex, are HIV positive but complex, are HIV positive but asymptomatic, and normal controls: asymptomatic, and normal controls:

Fat AbsorptionFat Absorption

Keys to RememberKeys to Remember

Plot both distributions using the same Plot both distributions using the same scale.scale.

Always compare apples to apples. By Always compare apples to apples. By that, I mean compare mean to mean, that, I mean compare mean to mean, median to median, Q1 to Q1, etc. median to median, Q1 to Q1, etc. Students lose points on the AP exam Students lose points on the AP exam when they make comparisons between when they make comparisons between two different measures.two different measures.

Now let’s compare…Now let’s compare…

Fat Absorption

HomeworkHomework

Chapter 2 #2, 5, 7, 9, 10Chapter 2 #2, 5, 7, 9, 10