ARITHMETIC MEAN, MEDIAN & MODE

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ARITHMETIC MEAN, MEDIAN & MODE. Presented By: ABID NAWAZ MERANI ABDULLAH OVAIS FARZAH SIDDIQUI SOAIYBA JABEEN AHMED B USINESS S TARS. INTRODUCTION TO ARITHMETIC MEAN. Given By: Abid Nawaz Merani. The raw data given below show the scores of an Australian Batsman of his last 30 matches.

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### ARITHMETIC MEAN, MEDIAN & MODE

Presented By:

ABID NAWAZ MERANI

ABDULLAH OVAIS

FARZAH SIDDIQUI

SOAIYBA JABEEN AHMED

### INTRODUCTION TO ARITHMETIC MEAN

Given By:

Abid Nawaz Merani

The raw data given below show the scores of an Australian Batsman of his last 30 matches.

60 71 52 67 89

79 73 49 62 66

78 90 72 58 65

76 81 69 80 57

54 73 61 73 45

51 63 60 76 85

Calculate the Mean, Median & Mode from

the above raw data and also draw graph.

Calculating RANGE:-

Maximum Value – Minimum Value = Range

90 – 45 = 45

Calculating NUMBER OF CLASSES:-

No. of Classes = 1 + 3.3 log10(n)

= 1 + 3.3 log10(30)

= 5.874 or 6 (approx)

Calculating WIDTH (h) :-

Width = Range

No. of Classes

Width = 45

5.874

Width = 7.66 or 8 (approx)

C - I Tele-Mark f

45 – 52 IIII 4

53 – 60 IIII 5

61 – 68 IIII I 6

69 – 76 IIII III 8

77 – 84 IIII 4

85 – 92 III 3

### ARITHMETIC MEAN

Further Explained By:

Farzah Siddqui

For Arithmetic Mean:-

Sum of the products of frequencies and

mid-points, divided by the sum of all

frequencies.

The Formula of Mean for group data is :

X = ∑ f x

∑ f

C - I f x fx

45 – 52 4 48.5 194.0

53 – 60 5 56.5 282.5

61 – 68 6 64.5 387.0

69 – 76 8 72.5 580.0

77 – 84 4 80.5 322.0

85 – 92 3 88.5 265.5

Total ∑ f = 30∑ f x = 2031

Calculating MID-POINT (x):-

Formula for the Mid-point

x1 + y1

2

Where,

“x1” can be 45, 53, 61, 69,77 or 85 and

“y1” can be 52, 60, 68, 76, 84 or 92 respectively.

45 + 52 => 48.5

2

Calculating Arithmetic Mean:-

X = ∑ f x

∑ f

X = 2031

30

X = 67.7

### MEDIAN

Explained By:

Soaiyba Jabeen Ahmed

FOR MEDIAN:-

C - I f C – B C - F

45 – 52 4 44.5 – 52.5 04

53 – 60 5 52.5 – 60.5 09

61 – 68 6 60.5 – 68.5 15

69 – 76 8 68.5 – 76.5 23

77 – 84 4 76.5 – 84.5 27

85 – 92 3 84.5 – 92.5 30

∑f = 30

FORMULA FOR MEDIAN:-

In case of frequency distribution:

Median = l + h ∑ f – C.F

f 2

Median Class:-

Median Class = ∑ f = 30 => 15

2 2

Where,

L = Lower class boundary of Median Class

h = Class Height

f = Frequency

∑f = Sum of frequency

C.F = Cumulative frequency of Preceding

class

By Putting The Values In The Formula,

X = 60.5 + 8 30 – 9

6 2

X = 68.5

### MODE

Explained By:

Abdullah Ovais

FOR MODE:-

C - I f C – B

45 – 52 4 44.5 – 52.5

53 – 60 5 52.5 – 60.5

61 – 68 6 60.5 – 68.5

69 – 76 8 68.5 – 76.5

77 – 84 4 76.5 – 84.5

85 – 92 3 84.5 – 92.5

∑ f = 30

FORMULA FOR MODE:-

In case of frequency distribution:

Mode = l + fm – f1 h

2fm – f1 – f2

Where,

L = Lower class boundary of Modal Class

h = Class Height

Fm = Frequency of modal class / Highest

frequency

f1 = Preceding frequency of Modal Class

f2 = Following frequency of Modal Class

By Putting The Values In The Formula,

X = 68.5 + 8 – 6 8

2(8) – 6 – 4

X = 71.16

Hence,

Mode > Median > Mean

71.16 > 68.5 > 67.7

GRAPHICAL REPRESENTAION:-

8-- HISTOGRAM

7--

F

R 6--

E

Q 5--

U

E4--

N

C3--

Y

2--

1--

44.5 52.5 60.5 68.5 76.5 84.5 92.5

CLASS BOUNDARIES

### EXAMPLE OF POSITIVELY SKEWED CURVE

Given By:

Soaiyba Jabeen Ahmed

### EXAMPLE OF SYMETRICAL CURVE

Given By:

Abid Nawaz Merani

PRESENTATION ENDED

We are very thankful to our respected teacher Mr. Zafar Ali and the students of our class for their precious time and kind attention and for maintaining the discipline throughout the Presentation. Please excuse, if anyone of us hurt you, we really didn’t mean it.