Calculating Averages with Continuous Data Example 1 A

Calculating Averages with Continuous Data

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 20 < t ≤ 30 30 < t ≤ 40 1 2 2 40 < t ≤ 50 50 < t ≤ 60 60 < t ≤ 70 70 < t ≤ 80 80 < t ≤ 90 90 < t ≤ 100 9 13 17 3 2 2

Estimating a minute - nurses results 18 F r e q u e n c y 16 14 12 10 8 6 4 2 0 10 20 30 40 50 60 Time (seconds) 70 80 90 100

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 2 40 < t ≤ 50 9 50 < t ≤ 60 13 60 < t ≤ 70 17 70 < t ≤ 80 3 80 < t ≤ 90 2 90 < t ≤ 100 2

Estimating a minute - nurses results 18 F r e q u e n c y 16 14 12 10 8 6 4 2 0 10 20 30 40 50 60 Time (seconds) 70 80 90 100

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

Estimated mean • grouped data so the mean is estimated. Time (seconds) Frequency Midpoint Mid-point x Frequency 10 < t ≤ 20 1 15 15 20 < t ≤ 30 2 25 50 30 < t ≤ 40 2 35 70 40 < t ≤ 50 9 45 405 50 < t ≤ 60 13 55 715 60 < t ≤ 70 17 65 1105 70 < t ≤ 80 3 75 225 80 < t ≤ 90 2 85 170 90 < t ≤ 100 2 95 190 Total 50 Estimated mean = sum of mid-point x freq = total frequencies 2945 = 58. 9 seconds 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.