1. WARM-UP Marina has the following quiz grades in her Discrete Math class: 84, 90, 96, 100, 67, 88, 90, 92, 94. Find the mean, median, mode, and standard deviation for Marina’s quiz grades. Mean=89 Median=90 Mode=90 SD=8.92

2. Histograms, Stem & Leaf, Box & Whiskers Day 2

3. Steam and Leaf Plot Method of arranging data in increasing or decreasing order “Stem” – left side of column which contains the tens digits “Leaf” – right side of column which contains the ones digits Must have a key

4. Example 1 – Data for Ages of People Online After Midnight 18456719 20357222 68273435 19212432 61552425 We want to use this data to create a stem and leaf plot

5. Ex 1 cont. - Stem & Leaf Plot 12345671234567 1845 6719 2035 7222 6827 3435 1921 2432 6155 2425 Stem 899899 01244570124457 24552455 2 5 178178 5 Leaf

6. Ex 2: Steam and Leaf Plot Create a steam and leaf plot with these values: 7.6 8.1 9.2 6.8 5.9 6.2 6.1 5.8 7.3 8.1 7.4 8.8 7.7 8.2 5678956789 **Steam & Leaf plots make no accommodations for decimals **ones digits = steam and tenths = leaf 8989 128128 34673467 11281128 2

7. You Try!!! Create a steam and leaf plot with these recent test scores: 73 42 67 78 99 84 91 82 86 94 456789456789 2 7 3838 246246 149149

8. Histogram Variation of a bar graph to arrange data Used for continuous variable We must use frequency tables to organize data before creating a histogram Must decide class intervals for data: Deciding data into reasonable increments Grouping data together Class intervals: Must be equal length Columns must touch because there aren’t any gaps between class intervals Value that falls on boundary between class intervals is called endpoint convention

9. How to make a Frequency Table Separate data into a range and counts the frequency (%) for each range. Class Interval Width= Relative Frequency=

10. Example 1 – Data for Ages of People Online After Midnight 18456719 20357222 68273435 19212432 61552425 We want to use this data to create a frequency table in order to draw a histogram There are 20 total data points therefore 5 intervals would make data reasonable to work with. Find interval width =

11. Frequency Table IntervalFrequency (# data points in class interval) Relative Frequency USE THIS TO DRAW A HISTOGRAM!!! 20 data points 5 class intervals with length of 11 17 - 28 28 - 39 39 - 50 50 - 61 61 - 72 10 4 1 2 3 50% 20% 5% 10% 15%

12. Ages Histogram

13. Box & Whiskers Plot Method of displaying data that uses quartiles (separate data) to form the center box Whiskers – minimum & maximum values

14. Steps to Create Box and Whiskers Plot 1) Order the data to find the median value 2) Divide the data into 2 parts using the median 1 st part of data – to the left of the median value 2 nd part of data – to the right of the median value 3) Find the median of each half of the data 4) Label the medians, minimum, maximum values of the data to draw the box and whiskers plot

15. Ex 1: Box and Whiskers Plot Make box and whiskers plot for these values 91 95 88 85 90 97 94 100 81 1) Order the data: 81 85 88 90 91 94 95 97 100 2) Label the data 3) Find the median of the first half of data and the second half of data 4) Draw Box and Whiskers Plot Minimum MaximumMedian Median=86.5Median=96

16. Ex 2: Box and Whiskers Plot Make box and whiskers plot for these values 84 79 90 73 95 88 92 81 67 1) Order the data: 67 73 79 81 84 88 90 92 95 2) Label the data 3) Find the median of the first half of data and the second half of data 4) Draw Box and Whiskers Plot Minimum MaximumMedian Median=76Median=91

17. You Try!!! Create a Box and Whiskers plot for these values 34 36 47 45 28 31 29 40 28 29 31 34 36 40 45 47 Minimum Maximum Median=35 Median=30Median=42.5