# Cumulative Frequency, Box Plots, Percentiles and quartiles.

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Cumulative Frequency, Box Plots, Percentiles and quartiles.
6.4 Cumulative Frequency, Box Plots, Percentiles and quartiles.

Cumulative Frequency Total frequency of all values less than or equal to a given value of the variable

Example Junโs parents decided to monitor the length of time that he spoke on the telephone. The table shows the time, to the nearest minute, that Jun spoke during his last 80 calls. Represent this information in a cumulative frequency table. Number of Minutes Upper Boundary Frequency Cumulative frequency 0-2 8 3-5 12 6-8 28 9-11 20 12-14 15-17 4

Example Create a cumulative frequency curve (0gives) Number of Minutes
Upper Boundary Frequency Cumulative frequency 0-2 2.5 8 3-5 5.5 12 20 6-8 8.5 28 48 9-11 11.5 68 12-14 14.5 76 15-17 17.5 4 80

Percentiles and Quartiles
Lower quartile: ๐ 1 , is found by finding ๐รท4 on the cumulative frequency axis, where n is the total frequency Median: finding ๐รท2 on the cumulative frequency axis Upper quartile: ๐ 3 , is found by finding 3๐รท4on the cumulative frequency axis Percentiles: are found by reading the value on the curve corresponding to ๐๐รท100 Interquartile range: subtract ๐ 3 - ๐ 1 , IQR

Time Frequency Cum. Freq. 0โค๐ก<1 3 1โค๐ก<2 5 2โค๐ก<3 7 3โค๐ก<4 9 4โค๐ก<5 22 5โค๐ก<6 28 6โค๐ก<7 8 7โค๐ก<8 8โค๐ก<9 6 9โค๐ก<10 4 10โค๐ก<11 2 11โค๐ก<12 1 100 students attempt to complete a jigsaw puzzle. The time (in minutes) that it takes each one is shown in the table. Construct a cumulative frequency table Draw a cumulative frequency graph Use your graph to estimate The lower quartile Median Upper quartile Interquartile range The 30th percentile.

Example From the cumulative frequency graph find The median
The interquartile range The 70th percentile

Box and whisker plots A visual way to show the spread of the data along with lower quartile, median, upper quartile, maximum and minimum. Minimum lower median upper maximum quartile quartile

Example

Outlier: a value that is much smaller or much larger than the other values.
Outliers Smaller than lower quartile โ 1.5 x IQR Larger than upper quartile x IQR

Represent the information on box plots Are there any outliers?
French Spanish Stem 8 2 3 8 9 4 0 5 5 6 7 9 4 8 This stem and leaf diagram shows the results, as percentages, for French and Spanish tests taken by 23 grade 7 students. Represent the information on box plots Are there any outliers?

Represent in a box and whisker plot (Use GDC) Are there any outliers?
The temperature each day, in degrees Celsius, at 12 noon in Tokyo in the month of July was: Represent in a box and whisker plot (Use GDC) Are there any outliers?

Assignment P.297 #1-3, 5,6, 7