5 Number Summary
What makes up the 5-number summary?
MIN, Quartile 1, Median, Quartile 3, MAX
What is the IQR & what does it tell us about our data set?
The InterQuartile Range is the difference between Q3 and Q1. Another way to see the spread of data.
How do you find the mean? Find the mean of the following data set: {6, 14, 18, 10, 16, 13, 20, 15, 9, 19}
You add all of the data points together and divide them by the number of observations in the data set Mean: 14
What does the whole area under the curve equal?
What are the steps in "backwards calculations" in Normal Distribution problems?
Prop Above --> Prop Below --> Z-Scores --> Data Point
What is the first thing that must be done to the data set?
Order the data from smallest to largest
What is the formula for IQR and IQR rule to get Outliers?
IQR formula: Q3-Q1
IQR Rule: lower: Q1 - (1.5 x IQR)
higher: Q3 + (1.5 x IQR)
What is the relationship between standard deviation and variance? If I have variance how can I get the standard deviation?
Standard deviation is the variance to the power of two, if you have variance just square it to get the standard deviation
Table A will tell you the area under the curve to the ________ of the _________
Left , Z-score
What are the steps in "forwards calculations" in Normal Distribution problems?
Data Point --> Z-Scores --> Prop Below --> Prop Above
Find the 5-number summary of this even-numbered data set: {13, 18, 42, 33, 43, 29, 46, 32, 12, 39}
Min: 12
Q1: 18
Med: 32.5
Q3: 42
Max: 46
If the data point is 1.5 x IQR above the max or 1.5 x IQR below the min
Do you need to have the data in order from smallest to largest to find the standard deviation, mean, or variance?
No the orde of the data points when solving SD, mean, or variance matters.
You are given a z-score of -0.67. Find the proportion to the left.
0.2514
Students take a math test and the scores recorded have a Normal Distribution with the average being a 90 with a standard deviation of 8. Find the minimum test score needed to be a part of the top 20%.
157.2
Find the 5-number summary of this odd-numbered data set: {3, 36, 0, 43, 25, 50, 40, 44, 47, 10, 46}
Min: 0
Q1: 10
Median: 40
Q3: 46
Max: 50
Find the IQR of the following data set: { 49, 16, 15, 4, 46, 43, 29, 38, 35, 11, 47, 50}
IQR: 31
Set up the columns used in the lecture to find the standard deviation
(observations) (deviations) (squared deviations)
xi (xi-mean) (xi-mean)2
You are given a z-score of 1.14. Find the proportion to the left.
1-.8729= 0.1271
Students take a math test and the scores recorded have a Normal Distribution with the average being a 90 with a standard deviation of 8. What is the probability that a student scores at most a 70 on this exam?
0.0062
What percentage of data can be found from the minimum to quartile 3?
75%
Is there an outlier in the following data set: {31, 23, 35, 36, 3, 14, 26, 33, 27, 47, 16, 0, 25}
There are no outliers
LF: Anything less than -13.5
UF: Anything above 62.5
Find the mean, standard deviation, and variance of the following data set: {6, 5, 19, 15, 17, 7, 8}
Mean: 11
SD: 5.80
Variance: 33.67
Find the area in between the z-scores
0.8729 - 0.2514= 0.6215
Students take a math test and the scores recorded have a Normal Distribution with the average being a 90 with a standard deviation of 8. The bottom 40% of students did not pass the course and the top 20% of students finished the course with the highest grade. What is the range of scores for the students in between? Z2
[88, 157.2]