Gr 10 Data Handling 3 - Maths Excellence

INDIVIDUAL
FORMATIVE
ASSESSMENT
Activity 1
1. For each set of data, determine the quartiles:
A 2 3 5 7 9 10 11 13 15 16 16 17 18 19 21 22 23 25 32
B 2 3 5 7 9 10 11 13 15 16 16 17 18 19 21 22 23
C 2 3 5 7 9 10 11 13 15 16 16 17 18 19 21 22 23 25 32 34
D 2 3 5 7 9 10 11 13 15 16 16 17 18 19 21 22 23 25
DVD
Lesson
Range
The range is the difference between the largest and the smallest value in the
data. The bigger the range, the more spread out the data is. The range cannot
be used with grouped data and it doesn’t deal with values between these
extremes. Also, a single very small or very large value would give a misleading
impression of the spread of the data.
Consider for example, the following set of marks for Class A:
Class A 1 1 2 2 3 4 4 5 5 6 7 8 8 9 10
Range = largest score – smallest score = 10 – 1 = 9
Deciles and percentiles
Deciles subdivide the data into tenths. Percentiles divide the data into
hundredths.
The interquartile range (IQR)
The difference between the lower and upper quartile is called the interquartile
range. It is a better measure of dispersion than the range because it is not
affected by extreme values. It is based on the middle half of the data. It
indicates how densely the data in the middle is spread around the median.
Example
Calculate the interquartile range for the following data set.
2 2 3 4 5 5 6 7 7 8 9
Lower
Quartile
Q 1
IQR = Q 3
– Q 1
= 7 – 3 = 4
The semi-interquartile range
Median
Q 2
Upper
Quartile
Q 3
The semi-interquartile range is half of the interquartile range.
The semi-IQR for the previous example is _
Q – Q 3 1
2
= _ 7 – 3 = 2.
2
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10 LC G10 MATHS LWB.indb 18 2008/09/09 12:22:45 PM