1. Measures of Central Tendency of Grouped Data, Standard Deviation, Histograms and Frequency Polygons

2. Univariate Data Concerned with a single attribute or variable.
Two forms of numerical data
DISCRETE data – collected by counting exact amounts
CONTINUOUS data – values form part of a continuous scale – generally collected by measurement

3. Grouped frequency Table
For large volume of data.
Group data in frequency table.
Groups should not overlap.
Use inequality signs for continuous data.

4. ORGANISING DATA Can organise data using
a stem and leaf diagram/display
A frequency table
A grouped frequency table
Data could be discrete or continuous

5. Activity 1 a) b) How many learners watched less than 11
hours of TV a week?
How many learners watched more than 20
Group
tally
frequency
0 -10 hrs
|||| |||| || 12
11 – 20 hrs
|||| |||| |||| 14
21 – 30 hrs
|||| 4
TOTAL 30

6. a) Continuous data b) c) 11 learners 2 3 6 7 5 Interval Tally
Frequency || 2
||| 3
|||| | 6
|||| || 7
|||| 5

7. Measures of Central Tendency from a Frequency Table
The Mean
We use the following formula to find the mean of ungrouped data:
Mean = = ,
where = sum of the data items,
and = the number of items
We use a modified formula when finding the mean of grouped data:
Mean = = , where = the frequency,
is the value of the item, and = the number of items

8. The median
The median is the middle data item when the
data is listed in order. We sometimes use the
formula to find out which item is the
middle item, and can also find the median
from the frequency table.
The mode
The mode is the data item with the highest
frequency.

9. Mark obtained x
Frequency f fx 10 1 20 2 40 80 3 50
150 4 30
120 5 6 7
140 8 9 90
100
n = 250
= 1 050

10. Mean = 4,2
Median = 4
Mode = 3

11. Activity 2 Mean no of children per family = 1 18th position, sox
No. of families f
Total no. of children fx 12 1 15 2 5 10 3 6 4
n = 35
Σfx = 35
Mean no of children per family = 1
18th position, so
Median = 1
Mode =1

12. Measures of Central Tendency from a Grouped Frequency Table
This means trees were from 2 to 4 m.
Total frequency = 40.
Median is 20½th item. So, median is in interval:
Height (h) in metres
Frequency 2 6 11 12 8 1
n=40
This is the group with the highest frequency in the table. So, Modal class is

13. Activity 3 ques 2 Height (in metres) Midpoint Frequency 3 2 6 5 30 711 77 9 12
108 8 88 13 1
n=40
∑ =322

14. Mean ≈ 8,05
Median is 20,5th item.
Median is in the interval
Median ≈
Modal class is

15. The Standard Deviation of Data in a Frequency Table
To set up a frequency table press the following keys:
[SHIFT] [SETUP]
Scroll down using ▼ arrow
[3:STAT] [1:ON]

16. Activity 4 3 a) Mean = 418g b) Standard deviation = 21g
(418 ± 21) = (418 – 21; )
= (397;439)
6 cans lie in this interval.
= 31%

17. Midpoint of the interval
Activity 5
Speed in km/h
Midpoint of the interval X
No. of cars f
50 < s ≤ 60 55 20
60 < s ≤ 70 65 27
70 < s ≤ 80 75 25
80 < s ≤ 90 85 54
90 < s ≤ 100 95 21
100 < s ≤ 110
105 15
110 < s ≤ 120
115 8
120 < s ≤ 130
125 5

18. 2. a) Mean ≈ ÷ 175 = 82 km/h
b) Median lies in 88th position, which is
between 80–89km/h.
This is approx 85 km/h.
i.e half of the drivers are driving at
85 km/h or more 3.
Standard deviation = 17,5
5. (82 ± 17,5) = (82 – 17,5; ,5)
= (64,5; 99,5)
~ 81%