JV Stats HW & Test # 2

JV Stats HW & Test # 2OUTLIER FORMULAS

BOX PLOTS

HISTOGRAMS

DESCRIBING A DISTRIBUTION (C.U.S.S.)

STANDARD DEVIATION AND VARIANCE

Create a Box Plot of this data.We need the 5# summary, which consists of the min,Q1,Med,Q3, max

Finding q1 and q2 the long way

Outlier formulas

Outliers

Boxplot of greed data

Boxplot of greed data

What if there was an outlier

How many text messages?Get an exact count of the number of text messages SENT & RECEIVED since 8:00 AM today.(this is not a trap, I promise)

Text MEssagesCreate a stemplot

Find the 5# summary

Find the mean

Create a Boxplot(make sure to check for outliers!)

Describe the distributionPer 2 text messages

Per 2Per 2 text messages

Per 2Per 2 text messagesPer 2

Per 2 text messagesSummary of Stats

5# summary

Per 2Per 2 text messagesPer 2

Boxplot

5#-summary

0,0,5.5,20,9657 & 96 are outliersPer 2Describe the distribution(C.U.S.S.)The median number of total text messages for our class was 5.5 while the mean was 13.3. Two students had very large text message totals of 57 & 96 which were outliers. Since we had some large text totals out distribution was strongly skewed to the right. The # of text messages ranged from 0 to 96. Per 2Per 3 text messagesPer 3

Per 3 text messagesPer 3

Per 3 text messagesPer 3

Per 3 text messagesSummary of Stats5# summaryPer 3

Per 3 text messagesPer 3

Boxplot5#-summary0,0,8,29,11782,94,117 are outliersPer 3

Describe the distribution(c.u.s.s.)The median number of total text messages for our class was 8 while the mean was 20.8. Three students had very large text message totals of 82, 94, & 117 which were outliers. Since we had some large text totals out distribution was strongly skewed to the right. The # of text messages ranged from 0 to 117. Per 3histogramsStemplot of per 2 Unit 1 Test ScoresPer 2

histogramsHistogramPer 2

histogramsCalculating Numerical SummariesPer 2

histogramsDescribe the Distribution(C.U.S.S.)Our distribution of test scores is skewed to the left and there appear to be no outliers. The median test score fell in the 80% to 89% range. The mean will be somewhat lower than the median due to the skew to the left. Scores for this test ranged from the 40s up to around 100%.Per 2histogramsCalculating Numerical SummariesPer 3

histogramsDescribe the Distribution(C.U.S.S.)Our distribution of the unit 1 test scores is skewed to the left and there appear to be no outliers. The median test score fell between 90% and 94% inclusive. Due to the skew to the left our mean score is less than the median. Scores ranged from the low 60s up to the high 90s Per 3Histogram(centered on #s)

PER 2Test #1

Per 4Per 2Splitting Stems was used in these stemplotsPeriod 2 test scores

Find the Median, also called Q269Period 2 test scores

Find Q1 which is median below the MedianFind Q3 which is median above the Median5979Period 2 test scores

Give the 5-# summary which isMin, Q1 , Q2 , Q3 , MaxIQR is the interquartile range

IQR = Q3 Q141,59,69,79,9720Period 2 test scores

Checking for Outliers. We have formulas to check high and low numbers TO CHECK for a LOW OUTLIER

Q1 1.5(IQR) any # smaller is an outlierTO CHECK for a HIGH OUTLIER

Q3 + 1.5(IQR) any # larger is an outlier

Create a box plot

Min, Q1 , Q2 , Q3 , MaxOutliersCreate a box plot of your test scoresStart with a number line below your box plot

Make your increments consistent

Draw the box accurately

Period 4 test scoresFind the Median, also called Q2

69Period 4 test scoresFind Q1 which is median below the MedianFind Q3 which is median above the Median

5983Period 4 test scoresGive the 5-# summary which isMin, Q1 , Q2 , Q3 , MaxIQR is the interquartile range

IQR = Q3 Q1

41,59,69,83,9724Period 4 test scoresChecking for Outliers. We have formulas to check high and low numbers TO CHECK for a LOW OUTLIER

Q1 1.5(IQR) any # smaller is an outlierTO CHECK for a HIGH OUTLIER

Q3 + 1.5(IQR) any # larger is an outlier

Create a box plot

Min, Q1 , Q2 , Q3 , MaxOutliersCreate a box plot of your test scoresStart with a number line below your box plot

Make your increments consistent

Draw the box accurately

Back-To-back stemplot

C.U.S.S.This acronym is used to compare two or more distributions(graphs)

C: centergive the mean and median

U: unusual featuresare there outliers?

S: shapeskewed left, skewed right, fairly symmetric.etc

S: spread..give the range.(max min)

Use the C.U.S.S. acronym to compare two or more distributionsPeriod 2 has a mean of 69.5 and period 4 has a mean of 69.7. Both classes have a median of 69. There are no outliers for either class. Both distributions are fairly symmetric. Both classes had a min score of 41 and a max score of 97.Find the 5 # Summary and check for outliers{3,5,2,6,5,1,9,7,4,2,3,23}If you need to, put them in order

1,2,2,3,3,4,5,5,6,7,9,235 # Summary {1,2.5,4.5,6.5,23}Mystery box plotHere is the 5 # summary of a distribution of a set of 12 numbers

{1,7,9,13,22}

a) Is it possible that there is no number 9 in the set of numbers? Explain.

Yes, since there is an even number of numbers in the set, there is no exact middle number.Example. {1,2,7,8,8,10,10,13,19,22}Mystery box plotHere is the 5 # summary of a distribution of a set of 23 numbers

{1,7,9,13,22}

a) Is it possible that there is no number 9 in the set of numbers? Explain.

No, since there is an odd # of numbers in the set, the median must be a number in the set.Create your set of dataCreate a set of data with 20 numbers.

Make sure there are 2 low outliers and 2 high outliers.

Show your outlier formulas to prove that your set meets these requirements.

Create a box plot of your data.QuartilesA Box Plot is made up of Q1, Q2, and Q3.

These are called quartiles because they split the box plot into 4 parts.

1234Q1Q2Q3Each of the 4 parts contain 25% of the dataStandard Deviation & VarianceConsider the following set of numbers

{1,1,2,2,3,4,5,6,7,9}

Find the Mean.

Find the distance each # is from your mean, square all those distances and add them up

Divide that sum by (n-1)..this is the Variance

Take the square root of the Variance. Now you have the Standard Deviation

Lets add #13 to the setNow the mean is not a whole number, makes the process a little more difficult

What is standard deviationIt is the average distance the set of numbers are from the mean.

It is a measure of spread.

Lower standard deviation means that the numbers in the set are grouped closely around the mean

High standard deviation means that the numbers in the set are widely spread and may possibly have outliersFind the standard deviation1,7,2,10,4,7

Find the standard deviations(Round Means to whole #)

Find the standard deviations(Round Means to whole #)

The Game of Greed

The Game of greed

Find the 5 # Summary {0,16,32,53,73}

Check for OutliersQ1 1.5(IQR).16 1.5(37) = -39.5 Q3 + 1.5(IQR).53 + 1.5(37) = 108.5There are NO OUTLIERS

Draw the Box Plot

Describe the distribution(C.U.S.S.)

The mean is 34.3 and the median is 32. There are no outliers. The distribution is fairly symmetric and the range is from 0 to 73.HistogramsHow many times did you go out to eat over the weekend?

Before we create our histogram we need to make a frequency table.

Create the histogram

Calculate the mean of a histogram

Describe the distribution (c.u.s.s.)

Different types of histogramsBars are centered on the numbersBars are for a given range

Your data will help you decide which type is better

Outfiers affect Range, Mean, Variance, and Standard Deviation. An outlier causes all these to increase or decrease

Outliers do not affect the median and IQR.Coin in a cup activityGiven 3 minutes for your strong hand and 3 minutes for your weak hand. How many quarters can you bounce in a cup? Is your strong hand better than your weak?To reduce bias student flipped a coin to determine whether they would use their strong or weak hands for the first 3 minutes. This is done because students may learn how to bounce their coins and get better the second time around.Coin in a cup activity

Coin in a cup activity

PER 2Coin in the cup activity

PER 2Compare the Strong and WeakC.U.S.S.The median of the strong is 3.5 and the median of the weak is 2. The mean of the strong is 4.1 and the mean of the weak is 3.5. There are no outliers. Both distributions are skewed to the right. The strong ranges from 0 to 12 and the weak ranges from 0 to 10.Find the Standard Deviation1,4,6,3,7,8,1,8,7

Check for outliers1,25,23,38,45,45,48,53,67,72,76

Check for outliers1,25,23,38,45,45,48,53,67,72,76

Create a boxplot1,25,23,38,45,45,48,53,67,72,76

Find the mean and median of a histogram

Find the mean and median of a histogram

USE THESE TO CHECK FOR OUTLIERSTexting challengeBOYS VS GIRLSPair up with a person from the opposite sex, one person will text and the other person will time using their stopwatch.then switch

Mama always said, Life is like a box of chocolates, you never know what youre gonna getThe girls were much faster at texting, they had a median texting speed of 31 seconds while the boys median was 50 seconds. Mean times were 31.3 for girls and 49.5 for boys. The girls mean and median were very close together which resulted in a fairly symmetric box plot while the boys boxplot was arguably symmetric but could also be considered slightly skewed right. Even though the boys had some very slow texting times, there were no outliers for boys or girls.Boys had a much larger range with texting times ranging from 23.4 seconds up to 99 seconds. Girls times were much more consistent ranging from 15 seconds to 46 seconds.

2014 per 2Times(seconds) to Text Phrase

Boys(25,31.5,40,45,120Girls(22,29,34,48,78)Per 2BOYSGIRLS2014Describe the Distribution(C.U.S.S.)

Also use this to compare multiple distributionsDescribe the Distribution(C.U.S.S.)Per 2

Times(seconds) to Text PhraseBoys(31,40,42,53,53)Girls(25,34,40.5,46.5,66)Per 4

BOYSGIRLS

Exit light, enter night, take my hand, were off to never neverland.The girls were slightly faster at texting than the boys, they had a median texting speed of 21.5 seconds while the boys median was 24.8 seconds. Mean times were 25.6 for girls and 27.5 for boys. Both boys and girls had their mean times slower than their median times which resulted in boxplots that were slightly right skewed. The girls slowest texting time of 58 seconds and the boys slowest time of 61.5 seconds were considered outliers.Both the boys and the girls had similar ranges of texting times with the girls at 12 seconds up to 58 seconds and boys from 15.2 seconds up to 61.5 seconds.2015 per 3

Girls

Boys