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DISCOVER . LEARN . EMPOWER
1
UNIT-
1
Global School of Finance & Accounting
M. Com
SUBJECT NAME: Quantitative Techniques
SUBJECT CODE: 24CMT605
Rachit Agarwal
ASSISTANT PROFFESOR
Median
MEDIAN
Median is a value which is centrally located in a
series, in a way that it divides the series into
two parts. One part comprises of values greater
than median value and the other part
comprises all the values smaller than the
median value
Ms. Rattan
Laxmi
Introductio
n
The MEDIAN, denoted M, is the middle value of the sample when the data are
ranked in order according to size. • Connor has defined as “ The median is that
value of the variable which divides the group into two equal parts, one part
comprising of all values greater, and the other, all values less than median” • For
Ungrouped data median is calculated as:
• For Grouped Data:
Ad
187
Calculation in individual
series
• Individual Series:
• To find the value of Median, in this case, the terms are arranged in ascending or
descending order first; and then the middle term taken is called Median.
• Two cases arise in individual type of series:
• (a) When number of terms is odd:
• The terms are arranged in ascending or descending order and then are taken as
Median.
• (b) When number of terms is even:
• In this case also, the terms are arranged in, order and then mean of two middle
terms is taken as Median
Ms. Rattan
Laxmi
Ad
ODD No. SERIES (22,16,18,13,15,19,17,20,23)
6
7
Ad
EVEN NO SERIES
(200,217,316,264,296,282,317,299)
8
9
Ad
Calculation in discrete
series
• Discrete Series:
• Here also the data is arranged in ascending or descending order; And the (N+1/2) term
is taken after finding cumulative frequencies. Value of variable corresponding to that
term is the value of Median.
• Calculation of Median in Discrete Series:
• After arranging the terms, taking cumulative frequencies, we take (N+1/2) and then
calculate.
• Steps to Calculate:
• (1) Arrange the data in ascending or descending order.
• (2) Find cumulative frequencies.
• (3) Find the value of the middle item by using the formula
• Median = Size of (N+1/2)th item
• (4) Find that total in the cumulative frequency column which is equal (N + 1/2)th or
nearer to that value.
• (5) Locate the value of the variable corresponding to that cumulative frequency This is
the value of Median.
Ms. Rattan
Laxmi
11
Ad
12
13
Ad
Calculation of Median –Discrete series
i. X, f
ii. Arrange the data in ascending or descending
iii. Calculate the cumulative frequencies.(cf)
order
.
iv. Apply the formula.
Example: Median of a
discrete data
x Frequency of class(f) Cumulative
frequencies(cf)
10 15 15
20 32 47
30- Median (answer) 54 101
40 30 131
50 19 150
150 Okk
Median class: size of N+1/2 th item 150+1/2= 75.5th item
Ad
Characteristics of Median
Unlike the arithmetic mean, the median can be computed from open-
ended distributions. This is because it is located in the median class-
interval, which would not be an open ended class
As it is not influenced by the extreme values, it is preferred in case of a
distribution having extreme values.
In case of the qualitative data where the items are not counted or
measured but are scored or ranked, it is the most appropriate measure
of central tendency
MEDIAN
Median is a value which is centrally located in a
series, in a way that it divides the series into
two parts. One part comprises of values greater
than median value and the other part
comprises all the values smaller than the
median value
Ms. Rattan
Laxmi
Ad
18
19
Ad
Calculation in continuous
series
• Continuous Series:
• In this case cumulative frequencies is taken and then the value from the class-interval in
which (N/2)th term lies is taken
Merits and demerits of
median
208
Merits of median Demerits of Median
1. Simplicity 1.lack of representative
character
2. Free from effect of extreme
value
2.Unrealistic
3. Certainty 3.Lack of algebraic treatment
4. Graphic presentation
Ad
Characteristics of Median
Unlike the arithmetic mean, the median can be computed from open-
ended distributions. This is because it is located in the median class-
interval, which would not be an open ended class
As it is not influenced by the extreme values, it is preferred in case of a
distribution having extreme values.
In case of the qualitative data where the items are not counted or
measured but are scored or ranked, it is the most appropriate measure
of central tendency
Quartiles
The values of a variate that divide the series or the distribution into four
equal parts are known as quartiles. Since three points are required to divide
the data into four equal parts, we have three quartiles Q1 , Q2 , Q3.
The first quartile (Q1 ):- it is known as a lower quartile, is the value of a
variate below which there are 25% of the observation and above
which there are 75% of the observations.
The second quartile (Q2 ):- it is known as a middle quartile or median, is
the value of a variate which divides the distribution into two equal parts. It
means there are 50% of the observations above it and 50% of the
observations below it.
The Third quartile (Q3 ):- it is known as an upper quartile, is the value of a
variate below which there are 75% of the observations and above which
there are 25% of the observations.
Ad
211
Median Decision Science- Business Statistics
Ad
Median Decision Science- Business Statistics
Percentiles
The value of a variate which divides a given series or distribution into
100 equal parts are known as percentiles. Each percentile contains 1%
of the total number of observations. Since ninety nine points are
required to divide the data into 100 equal parts, we have 99
percentiles, P1 to P10
Ad
28
29
Lecture Overview
In this Presentation, we will learn about:
Meaning of Mode
Methods to calculate Mode in Individual, Discrete and Continuous
Series ( For Grouped and ungrouped series)
Relationship between Mean, Median and Mode
Symmetrical and Asymmetrical Distribution
Ad
Ad

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Median Decision Science- Business Statistics

  • 1. DISCOVER . LEARN . EMPOWER 1 UNIT- 1 Global School of Finance & Accounting M. Com SUBJECT NAME: Quantitative Techniques SUBJECT CODE: 24CMT605 Rachit Agarwal ASSISTANT PROFFESOR Median
  • 2. MEDIAN Median is a value which is centrally located in a series, in a way that it divides the series into two parts. One part comprises of values greater than median value and the other part comprises all the values smaller than the median value Ms. Rattan Laxmi
  • 3. Introductio n The MEDIAN, denoted M, is the middle value of the sample when the data are ranked in order according to size. • Connor has defined as “ The median is that value of the variable which divides the group into two equal parts, one part comprising of all values greater, and the other, all values less than median” • For Ungrouped data median is calculated as: • For Grouped Data:
  • 4. 187
  • 5. Calculation in individual series • Individual Series: • To find the value of Median, in this case, the terms are arranged in ascending or descending order first; and then the middle term taken is called Median. • Two cases arise in individual type of series: • (a) When number of terms is odd: • The terms are arranged in ascending or descending order and then are taken as Median. • (b) When number of terms is even: • In this case also, the terms are arranged in, order and then mean of two middle terms is taken as Median Ms. Rattan Laxmi
  • 6. ODD No. SERIES (22,16,18,13,15,19,17,20,23) 6
  • 7. 7
  • 8. EVEN NO SERIES (200,217,316,264,296,282,317,299) 8
  • 9. 9
  • 10. Calculation in discrete series • Discrete Series: • Here also the data is arranged in ascending or descending order; And the (N+1/2) term is taken after finding cumulative frequencies. Value of variable corresponding to that term is the value of Median. • Calculation of Median in Discrete Series: • After arranging the terms, taking cumulative frequencies, we take (N+1/2) and then calculate. • Steps to Calculate: • (1) Arrange the data in ascending or descending order. • (2) Find cumulative frequencies. • (3) Find the value of the middle item by using the formula • Median = Size of (N+1/2)th item • (4) Find that total in the cumulative frequency column which is equal (N + 1/2)th or nearer to that value. • (5) Locate the value of the variable corresponding to that cumulative frequency This is the value of Median. Ms. Rattan Laxmi
  • 11. 11
  • 12. 12
  • 13. 13
  • 14. Calculation of Median –Discrete series i. X, f ii. Arrange the data in ascending or descending iii. Calculate the cumulative frequencies.(cf) order . iv. Apply the formula.
  • 15. Example: Median of a discrete data x Frequency of class(f) Cumulative frequencies(cf) 10 15 15 20 32 47 30- Median (answer) 54 101 40 30 131 50 19 150 150 Okk Median class: size of N+1/2 th item 150+1/2= 75.5th item
  • 16. Characteristics of Median Unlike the arithmetic mean, the median can be computed from open- ended distributions. This is because it is located in the median class- interval, which would not be an open ended class As it is not influenced by the extreme values, it is preferred in case of a distribution having extreme values. In case of the qualitative data where the items are not counted or measured but are scored or ranked, it is the most appropriate measure of central tendency
  • 17. MEDIAN Median is a value which is centrally located in a series, in a way that it divides the series into two parts. One part comprises of values greater than median value and the other part comprises all the values smaller than the median value Ms. Rattan Laxmi
  • 18. 18
  • 19. 19
  • 20. Calculation in continuous series • Continuous Series: • In this case cumulative frequencies is taken and then the value from the class-interval in which (N/2)th term lies is taken
  • 21. Merits and demerits of median 208 Merits of median Demerits of Median 1. Simplicity 1.lack of representative character 2. Free from effect of extreme value 2.Unrealistic 3. Certainty 3.Lack of algebraic treatment 4. Graphic presentation
  • 22. Characteristics of Median Unlike the arithmetic mean, the median can be computed from open- ended distributions. This is because it is located in the median class- interval, which would not be an open ended class As it is not influenced by the extreme values, it is preferred in case of a distribution having extreme values. In case of the qualitative data where the items are not counted or measured but are scored or ranked, it is the most appropriate measure of central tendency
  • 23. Quartiles The values of a variate that divide the series or the distribution into four equal parts are known as quartiles. Since three points are required to divide the data into four equal parts, we have three quartiles Q1 , Q2 , Q3. The first quartile (Q1 ):- it is known as a lower quartile, is the value of a variate below which there are 25% of the observation and above which there are 75% of the observations. The second quartile (Q2 ):- it is known as a middle quartile or median, is the value of a variate which divides the distribution into two equal parts. It means there are 50% of the observations above it and 50% of the observations below it. The Third quartile (Q3 ):- it is known as an upper quartile, is the value of a variate below which there are 75% of the observations and above which there are 25% of the observations.
  • 24. 211
  • 27. Percentiles The value of a variate which divides a given series or distribution into 100 equal parts are known as percentiles. Each percentile contains 1% of the total number of observations. Since ninety nine points are required to divide the data into 100 equal parts, we have 99 percentiles, P1 to P10
  • 28. 28
  • 29. 29 Lecture Overview In this Presentation, we will learn about: Meaning of Mode Methods to calculate Mode in Individual, Discrete and Continuous Series ( For Grouped and ungrouped series) Relationship between Mean, Median and Mode Symmetrical and Asymmetrical Distribution