cumulative frequency, box plots, percentiles and quartiles. 6.4
TRANSCRIPT
Cumulative Frequency, Box Plots, Percentiles and quartiles.
6.4
• Total frequency of all values less than or equal to a given value of the variable
Cumulative Frequency
• Jun’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.
ExampleNumber ofMinutes
UpperBoundary
Frequency
Cumulative frequency
0-2 8
3-5 12
6-8 28
9-11 20
12-14 8
15-17 4
• Create a cumulative frequency curve (0gives)
Example
Number ofMinutes
UpperBoundary
Frequency
Cumulative frequency
0-2 2.5 8 8
3-5 5.5 12 20
6-8 8.5 28 48
9-11 11.5 20 68
12-14 14.5 8 76
15-17 17.5 4 80
• Lower quartile: , is found by finding on the cumulative frequency axis, where n is the total frequency
• Median: finding on the cumulative frequency axis
• Upper quartile: is found by finding on the cumulative frequency axis
• Percentiles: are found by reading the value on the curve corresponding to
• Interquartile range: subtract -, IQR
Percentiles and Quartiles
• 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.
Time Frequency
Cum. Freq.
3
5
7
9
22
28
8
5
6
4
2
1
Example
• From the cumulative frequency graph find– The median– The interquartile
range– The 70th percentile
• A visual way to show the spread of the data along with lower quartile, median, upper quartile, maximum and minimum.
Box and whisker plots
Minimum lower median upper maximum
quartile quartile
Example
0 3 6 9 13 17
• Outliers– Smaller than lower quartile – 1.5 x IQR– Larger than upper quartile + 1.5 x IQR
Outlier: a value that is much smaller or much larger than the other values.
• 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?
French Spanish
Stem
8 2
7 5 2 3 8 9
3 2 2 1 4 0 5
9 6 5 1 0
5 1 2 3 3 8 9
7 4 3 2 6 3 4 4 5
9 5 2 1 7 0 6 7 8
5 3 8 1 2 2
9 4 8
31 28 30 27 46 32 31 28 30 27 30 278 30 31 30 30 28 29 32 27 29 30 31 30 32 27 29 30 31 30 28 31 31
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:
• P.297 #1-3, 5,6, 7
Assignment