Boxplots and Outliers Notes Common Core Math 1 Boxplots and Outliers Notes

Warm-up: There are 40 children and 12 adults going on a trip to New York City by car. Each car can hold a maximum of 5 people. What is the least number of cars needed for the trip?

HW Key: 1) Quantitative, cm 9) see graphs 2) Categorical 4) Quantitative, minutes 5) Quantitative, points 6) B 7) A 8) C 9) see graphs 10a) 50% live over 2.5 years and 50% live less than 2.5 years 10b) This will give her a range of the hamster lifespan.

HW Key (cont.): 11a) Mean = 37.5 11b) Min = 1, Q1 = 35.5, Med = 39.5, Q3 = 44, Max = 50 IQR = 8.5 11c) New Mean = 40.82 Min = 32, Q1 = 36, Med = 40, Q3 = 45, Max = 50 Mean changed more because the low value (1) which was removed affected the mean more than the median. Median is more positional.

Box Plot – sometimes called “box and whisker plot” splits the data into quartiles (25%) using the 5-number summary. The box-and-whisker plot below shows the distribution of test scores in a Math 1 class. A) Determine the median of the box-and-whisker plot. ______________   B) What percentage of students scored between 90 and 100? ____________ C) What percentage of students scored between 70 and 90? ___________

How to enter data and find the 5-number summary in Ti-84

a) What percent of the data is above 89? _____________ Construct a box and whisker plot given the following set of data. List the five number summary (min, Q1, median, Q3, and max) as well as the mean. 22, 62, 66, 86, 92, 70, 76, 85, 99 a) What percent of the data is above 89? _____________   b) What percent of the data is below 76? _____________ c) What percent of the data is above Q1? _____________   Min: __________ Q1: __________ Median: __________ Q3: __________ Max: __________ Mean: __________

Tell what would happen to the median if the following pairs of numbers were added to the box and whisker plot above. Circle one.   64 and 78: stay the same decrease increase 85 and 90: stay the same decrease increase 60 and 72: stay the same decrease increase 64 and 97: stay the same decrease increase

Outlier - an observation point that is distant from other observations. an observation that is smaller than the lower bound (LB) and bigger than the upper bound (UB) Lower Bound = LB = Q1 – 1.5(IQR) Upper Bound = UB = Q3 + 1.5(IQR)

4) Using the original 9 data values in #2, find the following: A) Do the data have any low outliers? Explain.   B) Do the data have any high outliers? Explain.   IQR = 1.5(IQR) = LB = UB =

A) Find the five number summary: 7) Below is a stem and leaf plot of the amount of money spent by 25 shoppers at a grocery store. A) Find the five number summary: B) Construct a box plot. Stem Leaf 3 6   1 7 8 9 2 4 5 10 11 Key: 4|2 = $42 Min: Q1: Med: Q3: Max:

Do the data have any low outliers? Explain. Find the following: Do the data have any low outliers? Explain. Do the data have any high outliers? Explain.     IQR = 1.5(IQR) = LB = UB =