Grouped Frequency Tables YEAR 11 MATHS REVISION Grouped Frequency Tables

Averages from Grouped Frequency Tables fx If you struggle to find the midpoint, add the two numbers in the group together and divide by 2 Eg 20 + 30 = 50 ÷ 2 =25 Multiply the midpoints of each group by the frequency to fill our fx column 5 X 20 270 600 560 660 15 25 35 45 55 Add up our fx and frequency columns to find their total…. *NOTE – NEVER ADD UP YOUR MIDPOINTS!!!!!!! 80 2130 Calculate an estimate for the mean average. Finally, all we have to do is divide our fx total, by the frequency total to give us our estimate of the mean…… 2130 ÷ 80 = 26.625 (Show your full calculator display and then round accurately if asked) This means we know we must add an fx column at the end of our table and multiply our frequency with the midpoints of the groups………

Frequency Polygon Draw a frequency polygon to represent this data. 5 (5,4) Draw a frequency polygon to represent this data. 15 (15,8) 25 (25,24) 35 (35,16) 45 (45,6) 55 (55,12) KEY POINTS….. Firstly, find the midpoints of the groups in the table (same as before). Then, plot the midpoints against the frequency on your graphs. *YOU MUST BE ACCURATE, USE A PENCIL AND CHECK THE SCALE!!! Finally, join up your points with a RULER & PENCIL, starting at the first point, stopping at the last. x x x x x x

Cumulative Frequency 18 x x 50 – 32 = 18 x x x x Now, all we need to do, is plot the END NUMBER of our groups, against the CUMULATIVE FREQUENCY…..C x x 50 – 32 = 18 x Then, we join up our points on our graph using a PENCIL, with a SMOOTH CURVE…. x x This means, which group has the MOST in the frequency column…… So the modal class interval is……. x Cumulative means to add up the numbers as you go along….. So all we need to do is add on each number as we go down…… 7 18 27 18 37 45 50

Histograms Now, we need to LABEL and SCALE our axes. FREQUENCY DENSITY always goes up the y axis. Our biggest FD value is 2 so we need to split our axis up evenly up to 2. 2 Frequency Density ÷ 5 0.8 1.5 EG 15-5 = 10 10 1 15 1.6 1 FREQUENCY DENSITY 10 2 5 1.2 0.5 When you see that it asks for a HISTOGRAM, the first thing we need to do is add a FREQUENCY DENSITY column. To calculate Frequency Density, we first need to find our CLASS WIDTHS. This is the difference between the largest number in the group and the smallest. Then, to calculate Frequency Density , divide the frequency by the class width. Length (minutes) Finally we draw a bar chart. The bars are as wide as the group in the table and go as high as the frequency density. So the first bar, goes from 0 to 5 and goes up to 0.8.