YEAR 11 MATHS REVISION Box Plots Cumulative Frequency with Box Plots

Drawing a Box plot A box plot is just another way of representing data. To do this we need 5 pieces of information…. LOWEST VALUE LOWER QUARTILE MEDIAN UPPER QUARTILE HIGHEST VALUE Sometimes we get lucky and they give us all this information!! So all we have to do is represent these values on the grid given to us, using straight, vertical lines… Once all the data is plotted, draw a box around the middle three lines, this represents our INTER-QUARTILE RANGE. *To calculate this if asked…… UPPER QUARTILE – LOWER QUARTILE = 60 – 24 = 36 Finally, join our LOWEST and HIGHEST lines to the box

Comparing Box plots This topic comes up often in one way or another!! When comparing box plots, ALWAYS compare two things…… 1)THE MEDIAN 2)THE INTER QUARTILE RANGE THE MEDIAN This is the AVERAGE value for the two sets of data you are comparing. Usually one Median is larger than the other, so write that as a sentence. *Mention what the values are though when comparing the median to ensure you get the mark. In this case, the medians are exactly the same, so our sentence might sound like… “On average, Adil and Dev scored the same amount of runs as their median is both 40”. THE INTER QUARTILE RANGE This is the difference between the UPPER QUARTILE and the LOWER QUARTILE. The smaller the inter quartile range means that the data is MORE CONSISTENT, as it represents half of the data. So we can see from our example, Dev’s scores were a lot more consistent than Adil’s, as his inter quartile range was = 24, whereas Adil’s inter quartile range is = 36 (b) Make two comparisons of the box plots _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

Drawing a Box plot REMEMBER - A box plot is just another way of representing data. To do this we need 5 pieces of information…. LOWEST VALUE LOWER QUARTILE MEDIAN UPPER QUARTILE HIGHEST VALUE With raw data like in this question, we have to find our 5 pieces of information, so lets start with the easiest. LOWEST VALUE HIGHEST VALUE MEDIAN – Middle value when in order. Thankfully, our numbers are already in order so we just have to find the middle *Remember, if there are 2 middle numbers we add them together and half it. Lower Quartile This means the value at ONE QUARTER of our data. So we need to find half, of the first half of our data….. We can see there are 7 numbers in the first half, so the middle number of them is 14. Upper Quartile This means the value at THREE QUARTERS of our data. So we need to find half, of the second half of our data….. We can see there are 7 numbers in the second half, so the middle number of them is 30.

Drawing a Box plot *THE SNEAKY QUESTION…… REMEMBER - A box plot is just another way of representing data. To do this we need 5 pieces of information…. LOWEST VALUE LOWER QUARTILE MEDIAN UPPER QUARTILE HIGHEST VALUE LOWEST VALUE We are given this so we can just place this straight on to our grid…. HIGHEST VALUE We are given this so we can just place this straight on to our grid…. MEDIAN We are given this so we can just place this straight on to our grid…. LOWER QUARTILE We are given this so we can just place this straight on to our grid…. UPPER QUARTILE This is where it gets sneaky. It doesn’t actually give us this value, however it tells us the INTER QUARTILE RANGE which is 38. This means that the difference between the LOWER QUARTILE and the UPPER QUARTILE, is 38. So all I need to do is add it on to the LOWER QUARTILE value which was 32. So = 70

Drawing a Box plot using a Cumulative Frequency curve This means we need to half our data and find the weight (g) using our curve MEDIAN = 170g REMEMBER - A box plot is just another way of representing data. To do this we need 5 pieces of information…. LOWEST VALUE LOWER QUARTILE MEDIAN UPPER QUARTILE HIGHEST VALUE We are given our highest and lowest values….. We have already found our median value in the previous part of the question….. So we just need our LOWER and UPPER QUARTILE values….. LOWER & UPPER QUARTILES Similar to the MEDIAN, we must use our CUMULATIVE FREQUENCY curve to find these values… LOWER QUARTILE This is the value at a quarter of the data, so to find this, half our data and then half it again….. UPPER QUARTILE This is the value at three quarters of the data, so this is the value halfway between the MEDIAN and the TOTAL. = 175g = 165g