The document defines and describes cumulative frequency distributions and measures of central tendency. It explains that a cumulative frequency distribution shows the total frequencies of data values up to and including each class. There are two types: less than, where the cumulative total increases from lowest to highest values, and greater than, where it increases from highest to lowest. Measures of central tendency summarize a data set in a single value near the center, including arithmetic mean, median, and mode. Several problems demonstrate calculating these measures from data sets.

1. Cumulative Frequency
Distribution
• The cumulative frequency is the total of frequencies, in
which the frequency of the first class interval is added to
the frequency of the second class interval and then the
sum is added to the frequency of the third class interval
and so on.
• Hence, the table that represents the cumulative frequencies
that are divided over different classes is called the
cumulative frequency table or cumulative frequency
distribution.
• Generally, the cumulative frequency distribution is used to
identify the number of observations that lie above or
below the particular frequency in the provided data set.

2. Types of Cumulative Frequency
Distribution
It is classified into two different types namely:
1. Less than cumulative frequency
2. Greater than cumulative frequency.

3. Less Than Cumulative Frequency:
•The Less than cumulative frequency distribution is
obtained by adding successively the frequencies of all the
previous classes along with the class against which it is
written.
•In this type, the cumulate begins from the lowest to the
highest size.
Greater Than Cumulative Frequency:
•The greater than cumulative frequency is also known as
the more than type cumulative frequency.
•Here, the greater than cumulative frequency
distribution is obtained by determining the cumulative
total frequencies starting from the highest class to the
lowest class.

4. Problem 1 (Less than type)

6. Problem 2 (Less than type)

8. Problem 3 (Less than type)

10. Problem 4 (More than type)

12. Problem 5 (More than type)

14. Measure of Central Tendency
• Usually when two or more different data sets
are to be compared it is necessary to condense
the data, but for comparison the condensation
of the data set into a frequency distribution
and visual presentation are not enough.
• It is then necessary to summarize the data set
in a single value.
• Such a value usually somewhere in the center
and represent the entire data set and hence it
is called measure of central tendency or
averages.

15. Types of Measure of Central
Tendency:
1. Arithmetic Mean
2. Geometric Mean
3. Harmonic Mean
4. Mode
5. Median

18. Problem 1
Solution:

20. Problem 2

21. Solution:

22. Problem 3

25. Assumed Mean
Method

27. Problem 4

31. Step Deviation
Method

33. Problem 5

37. Mode

39. Problem 1
Solution:

41. Problem:
Find the mode using this data
Solution: Mode is 15

44. Problem 5

48. Median