1. Calculating Averages with
Continuous Data

2. 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

3. Estimating a minute - nurses results18 16 14 12 10 8 6 4 2 F r e q u n c y
Time (seconds)

4. 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

5. Estimating a minute - nurses results18 16 14 12 10 8 6 4 2 F r e q u n c y
Time (seconds)

6. 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

7. 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
Estimated mean = sum of mid-point x freq =
total frequencies
= 2945 = 58.9seconds 50

8. 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.