5,8,12,15,15,18,20,20,20,30,35,40, Drawing a Dot plot

BOX PLOTS

MEDIAN UPPER QUARTILE LOWER QUARTILE LOWEST VALUE HIGHEST VALUE

LOWER QUARTILE MEDIAN UPPER QUARTILE 5 figure summary 1.Highest Value = 36 2.Lowest value = 9 3.Median = 15 4.Lower Quartile = 14 5.Upper Quartile = 16

LOWER QUARTILE MEDIAN UPPER QUARTILE Inter quartile Range = Upper Quartile – Lower Quartile = 16 – 14 = 2 5 figure summary 1.Highest Value = 36 2.Lowest value = 9 3.Median = 15 4.Lower Quartile = 14 5.Upper Quartile = 16

WHY? The IQR measures the middle 50% of our data Extreme values are therefore eliminated

BOX PLOTS

MEDIAN UPPER QUARTILE LOWER QUARTILE LOWEST VALUE HIGHEST VALUE

Why a box plot? This shows the inter-quartile range in relation to the median They can be used to compare different sets of data The smaller the IQR is, the more consistent the data will be

These box plots show how 2 classes performed in a test. Compare the two box plots A B

EXAMPLE 1 (An odd number of values) Andy records the length of time of his mobile phone calls over 1 week. All the times are in minutes: 5,8,12,15,16,16,18,20,21,25,30,35,36,40,50. Work out the median, the lower and upper quartiles from his data and draw a box plot.

5,8,12,15,16,16,18,20,21,25,30,35,36,40, IQR = 20 minutes LOWER QUARTILE UPPER QUARTILE

8,12,15,16,16,18,20,21,25,30,35,36,40,50 The median of the lower half =LOWER QUARTILE. The median of the upper half =UPPER QUARTILE The median is 20.5 There are 7 numbers in each half EXAMPLE 2 (An even number of values)

8,12,15,16,16,18,20,21,25,30,35,36,40,50 The median is 20.5 The median occurs between the 7 th & 8 th value The rule is (n+1)/2

FINDING OUTLIERS Work out 1.5 x IQR; 1.5 x 20 = 30 Outliers will be more than 30 above the UQ → = 65 ie outliers are above 65

FINDING OUTLIERS Work out 1.5 x IQR; 1.5 x 20 = 30 Outliers will be less than the LQ - 30 → 15 – 30 = -15 ie outliers are below -15

A symmetrical distribution This shows that the data is evenly spread about the median

A positive skew This shows that more of the data has smaller values

A negative skew This shows that more of the data will have larger values

5,8,12,15,15,18,20,20,20,30,35,40, Drawing a Dot plot