Do Now

Chapter 5 Section E and F

Vocabulary Relative frequency- frequency expressed as a fraction of the total frequency Cumulative frequency- sum of the frequency up until the event. Cumulative relative frequency- sum of the relative frequency up until the event.

CategoryFrequencyCumulative Frequency Relative Frequency Cumulative Relative Frequency Rap4 Country3 Rock6 Classical2 Total

CategoryFrequencyCumulative Frequency Relative Frequency Cumulative Relative Frequency Total

Create a frequency bar graph and draw the frequency polygon

Create a cumulative frequency graph

Summarizing Data Given : 3, 6, 5, 4, 5, 5, 6, 7, find the mean, median and mode.

Given a frequency chart; find mean, median, and mode. DataFreq.(F )( x) Total40

Do Now- Reminder DataFrequency Find the mean, median, and mode for this data

Given a grouped frequency chart; find the mean DataFreq.(F )( x) Total40

Given a grouped frequency chart; find the median Test MarkNumber of Students

Quartiles Lower Quartile (Q1) = 25% of total frequencies Median Value (Q2) = 50% of total frequencies Upper Quartile (Q3) = 75% of total frequencies. Ex: 1,2,3,3,3,4,5,6,6,6,7,8,9,9,10,12

Quartiles with Cumulative Frequency Charts

Measuring the Spread Maximum= Highest Number Minimum= Lowest Number Range= Maximum – Minimum Interquartile Range = Q3 – Q1 Ex: For the data set 1,1,1,2,2,3,4,6,6,7,8,8,8,9,10,find the a. median b. lower quartile c. upper quartile d. interquartile range

Practice 1.Find the interquartile range. 2.Find the 40% percentile.

Plot what you now know in a Box-and Whisker Plot

Example For the data set: 2,3,4,4,4,5,5,5,6,6,6,7,8,9,9,10, Create a Box-and-whisker plot.

Outlier Test Using Boundaries Upper boundary = Q x IQR “any data larger than this is an outlier” Lower boundary = Q1 – 1.5 x IQR “any data smaller than this is an outlier” This is designated with an asterik. Whiskers extend to the last value that is not an outlier

Example 1,1,1,2,2,2,3,3,3,3,5,5,8,9,25

Measuring Dispersion So far we have range and IQ that measure dispersion. Variance- average distance of the square of each data from the mean. Standard Deviation- square root of the variance. How far each value is from the mean

Steps Find the mean Subtract each value from the mean Square the differences Find the average of the squares Take the square root

Example 15, 20, 30, 35

Calculator steps STAT, Edit (enter) Clear List 1 and enter data into L1 Press keys: stat, >(calc), 1:1-var stats, 2 nd L1, enter (or stat, calc, enter, enter) Ex: 5,10,10, 15,15,20,30,35,35,40,40,45