Group DATA:
Mean (AVERAGE)
Step 1: Determine the midpoint
Step 2: Calculate the frequency x midpoint
Step 3: determine the total
Step 4: Determine the mean
Example 5
Class interval (In Rand)
Frequency
Midpoint
Frequency x Midpoint
0-100
3
50
150
100-200
5
150
750
200-300
12
250
3000
300-400
6
350
2100
400-500
4
450
1800
Total:
Calculating the mode (MODUS) – Value that has highest frequency in data set
Modal class (Modale klas) = class with the highest frequency
Note: There can be more than one modal class in grouped data
Cumulative
frequency
Highest class interval
Where:
i is the class width
Δ1 is the difference between the frequency of class mode and
the frequency of the class after the class mode
Δ2 is the difference between the frequency of class mode and
the frequency of the class before the class mode
Lmo is the lower boundary of class mode
Example: Find the mode
How to calculate the lower and upper boundary:
Step 1: Determine the size gap i.e the difference between lower boundary of one group and
upper boundary of next group -> In this case 1
Step 2: determine half of the size gap (0.5)
Step 3: for lower boundary -> subtract 0.5 from lowest value in group (11-0.5 = 10.5)
Calculate the Median (Mediaan)
-Need to draw a cumulative frequency graph – Kumulatiewe frekwensiegrafiek (ogief)
Step 1: Construct the cumulative frequency distribution.
Step 2: Decide the class that contain the median.
Class Median is the first class with the value of cumulative
frequency equal at least n/2.
Step 3: Find the median by using the following formula:
Cumulative frequency
Using a Graph:
Class interval (In Rand)
Frequency
Cumulative frequency
0-100
3
3
100-200
5
8
200-300
12
20
300-400
6
26
400-500
4
30
Step 1: Cumulative frequency = y -axis and klas eindpunt (the largest value in the interval)->
x-axis
Always start the curve at 0; 0
Question: How many learners spend less than R150 a month (answer = 5)
Question: how many learners spend more than R380? (answer: 30-25 = 5)
Question: use the graph to determine the median