1. ARITHMETIC MEAN, MEDIAN & MODE Presented By: ABID NAWAZ MERANI ABDULLAH OVAIS FARZAH SIDDIQUI SOAIYBA JABEEN AHMED BUSINESS STARS

2. INTRODUCTION TO ARITHMETIC MEAN Given By: Abid Nawaz Merani

3. 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.

4. Calculating RANGE:- Maximum Value – Minimum Value = Range 90 – 45 = 45 90 – 45 = 45 Calculating NUMBER OF CLASSES:- No. of Classes = 1 + 3.3 log 10 (n) = 1 + 3.3 log 10 (30) = 1 + 3.3 log 10 (30) = 5.874 or 6 (approx)

5. Calculating WIDTH (h) :- Width = Range Width = Range No. of Classes No. of Classes Width = 45 Width = 45 5.874 5.874 Width = 7.66 or 8 (approx) Width = 7.66 or 8 (approx)

6. C - I Tele-Mark f C - I Tele-Mark f 45 – 52 IIII 4 45 – 52 IIII 4 53 – 60 IIII 5 53 – 60 IIII 5 61 – 68 IIII I 6 61 – 68 IIII I 6 69 – 76 IIII III 8 69 – 76 IIII III 8 77 – 84 IIII 4 77 – 84 IIII 4 85 – 92 III 3 85 – 92 III 3

7. ARITHMETIC MEAN ARITHMETIC MEAN Further Explained By: Farzah Siddqui

8. 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 X = ∑ f x ∑ f ∑ f

9. C - I f x fx C - I f x fx 45 – 52 4 48.5 194.0 45 – 52 4 48.5 194.0 53 – 60 5 56.5 282.5 53 – 60 5 56.5 282.5 61 – 68 6 64.5 387.0 61 – 68 6 64.5 387.0 69 – 76 8 72.5 580.0 69 – 76 8 72.5 580.0 77 – 84 4 80.5 322.0 77 – 84 4 80.5 322.0 85 – 92 3 88.5 265.5 85 – 92 3 88.5 265.5 Total ∑ f = 30 ∑ f x = 2031 Total ∑ f = 30 ∑ f x = 2031

10. Calculating MID-POINT (x):- Formula for the Mid-point x 1 + y 1 x 1 + y 1 2Where, “x 1 ” can be 45, 53, 61, 69,77 or 85 and “y 1 ” can be 52, 60, 68, 76, 84 or 92 respectively. 45 + 52 => 48.5 45 + 52 => 48.5 2

11. Calculating Arithmetic Mean:- X = ∑ f x X = ∑ f x ∑ f ∑ f X = 2031 X = 2031 30 30 X = 67.7 X = 67.7

12. MEDIAN Explained By: Soaiyba Jabeen Ahmed

13. FOR MEDIAN:- C - I f C – B C - F C - I f C – B C - F 45 – 52 4 44.5 – 52.5 04 45 – 52 4 44.5 – 52.5 04 53 – 60 5 52.5 – 60.5 09 53 – 60 5 52.5 – 60.5 09 61 – 68 6 60.5 – 68.5 15 61 – 68 6 60.5 – 68.5 15 69 – 76 8 68.5 – 76.5 23 69 – 76 8 68.5 – 76.5 23 77 – 84 4 76.5 – 84.5 27 77 – 84 4 76.5 – 84.5 27 85 – 92 3 84.5 – 92.5 30 85 – 92 3 84.5 – 92.5 30 ∑f = 30 ∑f = 30

14. FORMULA FOR MEDIAN:- In case of frequency distribution: Median = l + h ∑ f – C.F f 2 f 2 Median Class:- Median Class = ∑ f = 30 => 15 2 2 2 2

15. Where, L = Lower class boundary of Median Class h = Class Height f = Frequency ∑f = Sum of frequency C.F = Cumulative frequency of Preceding class class

16. By Putting The Values In The Formula, X = 60.5 + 8 30 – 9 X = 60.5 + 8 30 – 9 6 2 X = 68.5 X = 68.5

17. MODE Explained By: Abdullah Ovais

18. FOR MODE:- C - I f C – B C - I f C – B 45 – 52 4 44.5 – 52.5 45 – 52 4 44.5 – 52.5 53 – 60 5 52.5 – 60.5 53 – 60 5 52.5 – 60.5 61 – 68 6 60.5 – 68.5 61 – 68 6 60.5 – 68.5 69 – 76 8 68.5 – 76.5 69 – 76 8 68.5 – 76.5 77 – 84 4 76.5 – 84.5 77 – 84 4 76.5 – 84.5 85 – 92 3 84.5 – 92.5 85 – 92 3 84.5 – 92.5 ∑ f = 30 ∑ f = 30

19. FORMULA FOR MODE:- In case of frequency distribution: Mode = l + fm – f 1 h 2fm – f 1 – f 2 2fm – f 1 – f 2

20. Where, L = Lower class boundary of Modal Class h = Class Height Fm = Frequency of modal class / Highest frequency frequency f 1 = Preceding frequency of Modal Class f 2 = Following frequency of Modal Class

21. By Putting The Values In The Formula, X = 68.5 + 8 – 6 8 2(8) – 6 – 4 2(8) – 6 – 4 X = 71.16 X = 71.16Hence, Mode > Median > Mean Mode > Median > Mean 71.16 > 68.5 > 67.7 71.16 > 68.5 > 67.7

22. GRAPHICAL REPRESENTAION:- 8-- HISTOGRAM 7--F R6-- E Q5-- U E4-- N C3-- Y2--1-- 44.5 52.5 60.5 68.5 76.5 84.5 92.5 44.5 52.5 60.5 68.5 76.5 84.5 92.5 CLASS BOUNDARIES CLASS BOUNDARIES

23. NEGATIVELY SKEWED CURVE:-

24. EXAMPLE OF POSITIVELY SKEWED CURVE Given By: Soaiyba Jabeen Ahmed

26. EXAMPLE OF SYMETRICAL CURVE Given By: Abid Nawaz Merani

28. 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. 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. READERS ARE THE LEADERS