Stats

Pop QuizTrue or False?Up or Down?Left or Right?Potatoes or French Fries?Coke or Pepsi?Summer or Winter?Justin Bieber or Selena Gomez?Red or Green?Day or Night?Giraffe or Monkey?

Grade Your QuizTrueDownRightFrench FriesPepsiSummerJustin BieberGreenDayMonkey

Measures of Central TendencyMean: sum of data values/number of data valuesMedian: middle value or mean of two middle valuesMode: most frequently occurring valueNow lets find the mean, median, and mode of your quiz scores.

OutlierA value that is substantially different from other data in the set.Which is an outlier in the set of values?32, 25, 87, 39, 19, 36, 18

QuartileOne of three values that divides a set of data into four parts. This data shows water temperatures of the ocean in Pensacola, Florida. Now lets find the lower quartile and upper quartile of your quiz scores.

Box PlotMethod of displaying data that uses quartiles to form the center box and the minimum and maximum values to form whiskers.Now lets make a box plot of your quiz scores.

RangeThe difference between the highest and lowest data values.86 56 = 30 The range is 30.Now lets find the range of your quiz scores.

Interquartile RangeThe difference between the first and third quartiles.83 60.5 = 22.5 The interquartile range is 30.Now lets find the interquartile range of your quiz scores.

Your TurnYou surveyed 9 of your friends and found out their ACT scores: 24, 19, 22, 31, 25, 24, 21, 18, 29a. Find the mean, median, and mode of the data.Mean: 23.6; Median: 24; Mode: 24b. Find the upper and lower quartiles of the data.Lower: 20; Upper: 27c. Make a box plot of the data.

d. What is the range of the data?13e. What is the interquartile range of the data?71831202427

Math Test Scores

Math Test Scores

Math Test Scores

Intro ActivityFor your set of data, do the following:Find the mean, median, modeFind the rangeFind the lower and upper quartileFind the interquartile range

Set 17778798080818283Set 2206070808090100140Set 3506070808090100110Set 42030408080120130140

Intro ActivityAre the sets the same?What does the range tell you about the sets?Find two sets that are spread out differently, but their range is the same.Find two sets that are spread out differently, but their interquartile range is the same.

Set 17778798080818283Set 2206070808090100140Set 3506070808090100110Set 42030408080120130140

The Normal DistributionA normal distribution of data means that most of the points in a set of data are close to the "average," while relatively few points tend to one extreme or the other.

Different Normal DistributionsMost data close to meanData spread out

Standard DeviationThe standard deviation ( ) is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the data are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small.When the data are spread apart and the bell curve is more flat, that tells you you have a relatively large standard deviation.

One standard deviationOne standard deviation away from the mean in either direction on the horizontal axis (the red area on the above graph) accounts for somewhere around 68 percent of the people in this group. One standard deviation

Two standard deviationsTwo standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. Two standard deviations

Three standard deviationsThree standard deviations (the red, green and blue areas) account for about 99 percent of the people. Three standard deviations

Mens Heights69Mean is 69Standard Deviation is 2.871.874.677.466.263.460.6

Mens Heights69Michael Jordan is 78 tall71.874.677.466.263.460.6

OutlierA value that is substantially different from other data in the set.Michael Jordans height is an outlier.

Womens Heights63.6Mean is 63.6Standard Deviation is 2.566.168.671.161.158.656.1

The standard deviation of mens heights is 2.8The standard deviation of womens heights is 2.5What does this tell you about how the distributions compare?

Example 1An average light bulb manufactured by the Acme Corporation lasts 300 days with a standard deviation of 50 days. Sketch the normal curve for this distribution, labeling the x-axis with the values that are one, two, and three standard deviations from the mean. 300350400450250200150

Example 2An average IQ is 100 with a standard deviation of 10.Sketch the normal curve for this distribution, labeling the x-axis with the values that are one, two, and three standard deviations from the mean.

100110120130908070

Example 3Your production plant employs several seamstresses whose production rate is a normal distribution with a mean (x) of 50 jeans per month and a standard deviation ( ) of 3 jeans.

About what percent of the seamstress produce between 47 and 53 jeans per month?68%

b) What is the probability that a seamstress selected at random will produce more than 56 jeans per month?2.5%

c) What is the probability that a seamstress selected at random will produce between 44 and 47 jeans per month?13.5%

Conclusions Lap TimesRacer A has a mean lap time of 20 seconds, with a standard deviation of 2.1 seconds.Racer B has a mean lap time of 21 seconds with a standard deviation of 3.2 seconds.What can you conclude about the two racers?

Normal CurveThe mean and median are the SAME.

Mean balance pointMedian cuts area under curve in half

A football team has the following scores for their season: 28, 39, 49, 10, 52, 0, 3, 35, 46, 38.Find the mean of the scores.The team won 7 games and lost 3 games. In the games they lost, they scored 0, 3, and 10 points. Find the mean of the scores of the games they won.How do the means compare?

Negatively SkewedThe low outliers pull the mean down.

Positively SkewedThe high outliers pull the mean up.

Positively skewed, negatively skewed or normal?

Positively skewed, negatively skewed or normal?

Positively skewed, negatively skewed or normal?

Positively skewed, negatively skewed or normal?

Positively skewed, negatively skewed or normal?

Positively skewed, negatively skewed or normal?

Calculating Standard DeviationWorksheet