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