Calculating Averages with Continuous Data

Time (seconds) Frequency Example 1 A group of 50 nurses were asked to estimate a minute. The results are shown in the table. Time (seconds) Frequency 10 < t ≤ 20 1 20 < t ≤ 30 2 30 < t ≤ 40 40 < t ≤ 50 9 50 < t ≤ 60 13 60 < t ≤ 70 17 70 < t ≤ 80 3 80 < t ≤ 90 90 < t ≤ 100

Estimating a minute - nurses results 18 16 14 12 10 8 6 4 2 F r e q u n c y 10 20 30 40 50 60 70 80 90 100 Time (seconds)

Use the end points of each class interval for the scale on the horizontal axis Time (seconds) Frequency 10 < t ≤ 20 1 20 < t ≤ 30 2 30 < t ≤ 40 40 < t ≤ 50 9 50 < t ≤ 60 13 60 < t ≤ 70 17 70 < t ≤ 80 3 80 < t ≤ 90 90 < t ≤ 100

Estimating a minute - nurses results 18 16 14 12 10 8 6 4 2 F r e q u n c y 10 20 30 40 50 60 70 80 90 100 Time (seconds)

Averages Mode – with grouped data this is called the modal group or class. Time (seconds) Frequency 10 < t ≤ 20 1 20 < t ≤ 30 2 30 < t ≤ 40 40 < t ≤ 50 9 50 < t ≤ 60 13 60 < t ≤ 70 17 70 < t ≤ 80 3 80 < t ≤ 90 90 < t ≤ 100 Modal group 60 < t ≤ 70

Estimated mean Total 50 2945 grouped data so the mean is estimated. Time (seconds) Frequency 10 < t ≤ 20 1 20 < t ≤ 30 2 30 < t ≤ 40 40 < t ≤ 50 9 50 < t ≤ 60 13 60 < t ≤ 70 17 70 < t ≤ 80 3 80 < t ≤ 90 90 < t ≤ 100 Mid- point 15 25 35 45 55 65 75 85 95 Mid-point x Frequency 15 50 70 405 715 1105 225 170 190 Total 50 2945 Estimated mean = sum of mid-point x freq = total frequencies = 2945 = 58.9seconds 50

1: Find the modal group, median and estimate the mean from the table below. 2: Draw a graph to represent the data . Michelle keeps a record of the number of minutes her train is late each day. The table shows her results for a period of 50 days.