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

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

3. Example
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.
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

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

5. Percentiles and Quartiles
Lower quartile: 𝑄 1 , is found by finding 𝑛÷4 on the cumulative frequency axis, where n is the total frequency
Median: finding 𝑛÷2 on the cumulative frequency axis
Upper quartile: 𝑄 3 , is found by finding 3𝑛÷4on the cumulative frequency axis
Percentiles: are found by reading the value on the curve corresponding to 𝑝𝑛÷100
Interquartile range: subtract 𝑄 3 - 𝑄 1 , IQR

6. Time
Frequency
Cum. Freq.
0≤𝑡<1 3
1≤𝑡<2 5
2≤𝑡<3 7
3≤𝑡<4 9
4≤𝑡<5 22
5≤𝑡<6 28
6≤𝑡<7 8
7≤𝑡<8
8≤𝑡<9 6
9≤𝑡<10 4
10≤𝑡<11 2
11≤𝑡<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.

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

8. 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

9. Example

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

11. 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?

12. 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?

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