Grouped Data

Grouped data is when you are turning an interval into an average of the data. this is used

Example 1

Time taken to complete a chess game is as follows:

time	10-15	15-20	20-25	25-30	30 - 35
frequency	2	20	18	10	5

To find the tendency, we must first think. I dont know the time values they give me, because they are interval. I should average out the time. so interval 10→15 = 12.5 interval 15→20 = 17.5

so if we summed all the data: $12.5\ast 2+17.5\ast 20+22.5\ast 18+27.5\ast 10+32.5\ast 5=1217.5$ The average is the sum divided by the total # of data points. $avg=\frac{1217.5}{55}=22.136$ since grouped data is the midpoint of the interval, it gets less accurate as the interval gets larger