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Statistical Diagrams Boxplots

Statistical Diagrams Why do we use statistical diagrams? Statistical diagrams - are a good way to graphically summarise data - easy to read makes - easy to compare with other data What types of statistical diagrams is there? Line graph, bar graph, stem and leaf diagram, pie charts, box plots

Box and Whisker Plot Box and whisker plots A box and whisker plot is used to display information about the range, the median and the quartiles. It is usually drawn alongside a number line, as shown - A box and whisker plot is used to display information about the range, the median and the quartiles To plot a box plot we need: minimum value, lower quartile (Q1), median, upper quartile (Q3) and the maximum value.

Minimum and maximum Values Example: What are the maximum and minimum values of the following data? Maximum = 9 Minimum = 3

Median When ordered in size the median is the centre number. You can find the place using the formula: Example : Find the median of the data: Values 4 th term 3 Values If there is an even number of data values find the average of the two centre values Example: Find the median of the data: 12 values Values 6.5 th term 6 Values 7 values

Lower Quartile The lower quartile (Q1) is found by considering only the bottom half of the data, below the median. To Find the lower quartile you must find the median value of this part of the data Median 3.5 th term 3 values

Upper Quartile The upper quartile (Q3) is the median of the upper half of the data, above the median. To find the upper quartile it is similar to finding the lower quartile however, this time you use the upper half above the median Q1Q1 MedianQ3Q3

Inter-quartile Range Is another measure of the spread of values in the data set Inter quartile range = 9 – 5.5 = 3.5

Examples Example: Find the median and quartiles for the data below Median = 8 Lower Quartile = 5.5 Upper Quartile =

Example : Find the median and quartiles for the data below

Example 1: Find the median and quartiles for the data below and draw the box plot cm

Example 2: Find the median and quartiles for the data below and draw the box plot

Example 3: Find the median and quartiles and inter-quartile range for the data below and draw box plot Median = 18 Lower Quartile = 9.5 Upper quartile = 26 min = 3 max = 30 Semi-quartile range = 26 – 9.5 = 16.5

Example 4: Find the median and quartiles and inter-quartile range for the data below and draw box plot Median = 8.5 Lower Quartile = 4.5 upper quartile = 11 min = 1 max = 15 Semi-quartile range = 11 – 4.5 = 6.5