1) Frequency density is calculated by taking the frequency and dividing it by the class width. This allows frequencies to be presented in a more compact way. 2) Using data on the mass of 35 people, the document calculates the frequency densities for different mass ranges. The densities are 1/3, 2/3, 1/2, 1, and 1/3. 3) A histogram is drawn with the mass ranges on the x-axis and the frequency densities on the y-axis. The area under the histogram represents the total frequency, and is calculated by multiplying the frequency density by the class width for each range.

1. Tobby Gondwe
ZACODE
Calculating Frequency Densities

2. Introduction
 Frequency density is a way of presenting the
frequency in a compacted way.
 To calculate frequency density, we use the
formula:
 Frequency Density =
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝐶𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ

3. Example
 The table shows mass of 35 people in Kg
Mass
(Kg)
6 – 8 9 – 11 12 – 17 18 – 20 21 – 29
Frequenc
y
4 6 10 3 12

4. Frequency Densities
 To calculate the frequency densities, we use a
table as shown here:
Mass (Kg) Class width Frequency Frequency
Density
6 – 8 3 4 4
3
= 1
1
3
9 – 11 3 6 6
3
= 2
12 – 17 6 10 10
6
= 1
2
3
18 – 20 3 3 3
3
= 1
21 – 29 9 12 12
9
= 1
1
3

5. Frequency Densities
 The frequency Densities calculated from the
above slide are:
1
1
3
, 2, 1
2
3
, 1 and 1
1
3
The frequency densities have the same common
denominator. It would be easy for us to use it in the
next determination.
The vertical axis will be divided into thirds. 3 thirds
will make a 1 and so on. Note that the highest is 2.

6. Class boundaries
 Using the lowest class width, we determine the
class boundaries.
 Since our lowest mass is 6, our first class
boundary is 5.5.
 To find the second, we add 3(lowest class width)
to 5.5 and get 8.5.
 We continue adding 3 and get the following class
boundary values:
 5.5, 8.5, 11.5, 14.5, 17.5, 20.5, 23.5, 26.5 and
29.5.

7. Drawing the Histogram
On the Horizontal axis:
As seen from the class boundary values,
 the one with class width 6, takes up two classes
from 11.5 to 17.5 and
 the one with class width 9 takes up three classes
from 20.5 to 29.5.
 The rest of the classes take up one class each

8. Histogram
 In the end the histogram appears as shown here:

9. Area Under the Histogram
 To calculate the area under the histogram, we
use the formula:
 Area = height of bar(Frequency density) X Class
width.
 For example, the class for 12 to 17 Kg,
 Frequency density = 1
2
3
and the class width is
6(that is; 17.5 – 11.5 = 6)

10. Area under the Histogram
 Area = frequency density X class width
Area = 1
2
3
X 6
Area =
5
3
x 6
Area =
30
3
Area = 10
 As we can see, this is the frequency for the class
12 to 17.

11. Remember!
Area ∝ Frequency!
 Thank you!