2. is the science of the collection, organization, and
interpretation of data. It deals with all aspects of
this, including the planning of data collection in terms of
the design of surveys and experiments.
3. STATISTICS
Class intervals
a set of numerical data that is grouped
into several classes and the range of
each class is known as class interval
4. There should be between 5 and 20 classes.
The class width should be an odd number. This will
guarantee that the class midpoints are integers instead of
decimals.
The classes must be mutually exclusive. This means that
no data value can fall into two different classes
5. The classes must be all inclusive. This means that all data
values must be included.
The classes must be continuous. There are no gaps in a
frequency distribution. Classes that have no values in
them must be included (unless it's the first or last class
which are dropped).
The classes must be equal in width.
6. Class intervals
Find the largest and smallest values
Compute the Range = Maximum - Minimum
Select the number of classes desired. This is usually
between 5 and 20.
Find the class width by dividing the range by the number
of classes and rounding up.
Pick a suitable starting point less than or equal to the
minimum value.
7. STATISTICS
The data below shows the marks obtained by 40 students
in a monthly test.
99 88 75 92 58 75 80 70
64 42 70 58 90 68 50 78
43 89 45 93 61 81 58 65
69 76 88 58 91 67 71 52
55 40 80 80 78 46 61 69
8. STATISTICS
The lowest value : 40
The highest value : 99
Difference : 99-40 = 59
Width of class : 5 5959
5
Number of class intervals = 5
12
9. The lowest value : 40
The highest value : 99
Difference : 99-40 = 59
Width of class : 10
Number of class intervals = 59
10
6
10.
11. Class Limit
- Lower limit : the lowest value of the class interval
- Upper limit: the highest value of the class interval
13. Class Boundary
-lower boundary is the midpoint between the lower limit of
the class interval and the upper limit of the previous class
interval
- Upper boundary is the midpoint between the upper limit of
the class interval and the lower limit of the succeeding
class interval
17. HISTOGRAM
bar chart with
i. horizontal axis represented by the upper boundary and
the vertical axis represented by the frequency
Or
ii. frequency versus midpoint
18. Histogram
Histogram of marks
10
9
8
7
6
frequency
5
4
3
2
1
0
29.5-39.5 39.5-49.5 49.5-59.5 59.5-69.5 69.5-79.5 79.5-89.5 89.5-99.5
Upper boundary(marks)
19. HISTOGRAM
10 Histogram of Marks
9
8
7
Frequency
6
5
4
3
2
1
0
44.5 54.5 64.5 .74.5 84.5 94.5
midpoints ( marks )
20. Frequency polygon
is a closed line graph
Two methods :
i. From histogram
ii. frequency versus midpoint
21. Histogram and Frequency polygon
10
9
8
7
6
Frequency
5
4
3
2
1
0
29.5-39.5 39.5-49.5 49.5-59.5 59.5-69.5 69.5-79.5 79.5-89.5 89.5-99.5 99.5-109.5
Upper boundary (marks )
22. Frequency polygon
Frequency polygon of marks
10
9
8
7
Frequency
6
5
4
3
2
1
0
34.5 44.5 54.5 64.5 .74.5 84.5 94.5 104.5
Midpoint (marks)
24. Ogive : Cumulative frequency curve
Cumulative frequency versus upper boundaries
25. Ogive of marks
45
40
35
Cumulative frequency
30
25
20
15
10
5
0
29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5
Upper boundary ( marks )
26. Measures of Dispersion
- the amount or distances the values are spread out in a set
of data
i. Range :midpoint of the highest class – midpoint of
the lowest class
ii. Median : the value at half of the distribution
iii. First quartile(Q1): the value at the first quarter
iv. Third quartile (Q3): the value at the third quarter
v. Interquartile range : Q3 – Q1
27. Ogive of marks
45
40
35
Cumulative frequency
30
25
20
15
10
5
0
29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5
Upper boundary ( marks )
