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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.
Types of Cumulative Frequency
Distribution
It is classified into two different types namely:
1. Less than cumulative frequency
2. Greater than cumulative frequency.
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.
Problem 1 (Less than type)
Problem 2 (Less than type)
Problem 3 (Less than type)
Problem 4 (More than type)
Problem 5 (More than type)
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.
Types of Measure of Central
Tendency:
1. Arithmetic Mean
2. Geometric Mean
3. Harmonic Mean
4. Mode
5. Median
Problem 1
Solution:
Problem 2
Solution:
Problem 3
Assumed Mean
Method
Problem 4
Step Deviation
Method
Problem 5
Mode
Problem 1
Solution:
Problem:
Find the mode using this data
Solution: Mode is 15
Problem 5
Median
Unit 3.pptx
Unit 3.pptx
Unit 3.pptx
Unit 3.pptx
Unit 3.pptx
Unit 3.pptx
Unit 3.pptx

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Unit 3.pptx

  • 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)
  • 5.
  • 6. Problem 2 (Less than type)
  • 7.
  • 8. Problem 3 (Less than type)
  • 9.
  • 10. Problem 4 (More than type)
  • 11.
  • 12. Problem 5 (More than type)
  • 13.
  • 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
  • 16.
  • 17.
  • 19.
  • 23.
  • 24.
  • 26.
  • 28.
  • 29.
  • 30.
  • 32.
  • 34.
  • 35.
  • 36.
  • 37. Mode
  • 38.
  • 40.
  • 41. Problem: Find the mode using this data Solution: Mode is 15
  • 42.
  • 43.
  • 45.
  • 46.
  • 47.