Outliers
A set of data has the following 5-number summary
Min = 0
Q1 = 6
Med = 8
Q3 = 9
Max = 10
Is 0 an outlier? Explain.
Yes
Outliers exist whenever less than Q1 - 1.5*IQR
6-1.5(3)=1.5
Since 0<1.5, 0 is an outlier.
What does a z-score represent?
The number of standard deviations above or below the mean.
The weights of Polar Bears is normally distributed with a mean of 990 pounds and a standard deviation of 95 pounds. In what percentile is a Polar Bear that weighs 1150 pounds?
z=(1150-990)/95=1.68
P(X<=1150)=0.9535=95.35%
A set of data has the following statistics.
Mean = 12
Stand. Dev. = 2.4
Is the data point 16 an outlier? Explain.
No.
12 + 2(2.4) = 16.8
Only data points greater than 16.8 are outliers.
What is the probability of an event that has a z-score of -0.75?
22.66%
The weights of Polar Bears is normally distributed with a mean of 990 pounds and a standard deviation of 95 pounds. What is the probability that a Polar Bear will weigh 1000 pounds or less?
z=(1000-990)/95=0.11
P(X<=1000)=0.5438=54.38%
A survey was given to determine the extent to which students like math at ESUMS. The following data was gathered.
Mean = 7.2
Stand. Dev. = 1.4
The highest data point was a 10. Is 10 an outlier?
No.
Upper Outliers > Mean + 2 Stand. Dev.
7.2+2(1.4)=10
What is the probability of an event with a z-score of 0.5?
69.15%
The weights of Polar Bears is normally distributed with a mean of 990 pounds and a standard deviation of 95 pounds. What is the probability that a Polar Bear will weigh more than 1075 pounds?
z1075=(1075-990)/95=0.89
P(X<=1075)=0.8133=81.33%
P(X>1075)=100%-81.33%=18.67%
A set of data has the following statistics.
Mean = 5.17
Stand. Dev. = 0.74
Data values within what interval(s) would be considered outliers?
5.17+2(0.74)=6.65
Lower Outliers = Mean - 2 Stand. Dev.
5.17-2(0.74)=3.69
Upper Outliers > 6.65
Lower Outliers < 3.69
What z-score has a probability of 98.96%?
z=2.31
The weights of Polar Bears is normally distributed with a mean of 990 pounds and a standard deviation of 95 pounds. What is the probability that a Polar Bear will weigh between 800 and 900 pounds?
z800=(800-990)/95=-2
P(X<=800)=0.0228=2.28%
z900=(900-990)/95=-0.95
P(X<=900)=0.1711=17.11%
P(800<X<900)=17.11%-2.28%=14.83%
Consider the following data:
68, 74, 80, 92, 85, 95, 78, 88, 83, 90
No.
Mean = 83.3
Stand. Dev. = 8.4
Lower Outliers < 83.3-2(8.4)=66.5
68>66.5, so 68 is not an outlier.
What z-score has a probability of 5%?
z=-1.64
The weights of Polar Bears is normally distributed with a mean of 990 pounds and a standard deviation of 95 pounds. What is the probability that a Polar Bear will weigh somewhere between 900 pounds and 1100 pounds?
z900=(900-990)/95=-0.95
P(X<=900)=0.1711=17.11%
z1100=(1100-990)/95=1.16
P(x<=1100)=0.8770=87.70%
P(900<X<1100)=87.70-17.11=70.59%