GROUP B (B.TECH) presentation for students.pptx

Chemistry lecture

1. GROUP "B" ATTQA BSBT 3-23-018 MARYAM BSBT 3-23-014 FARHANA BSBT 3-23-027 BIOTECHNOLOGY (4TH SEMESTER) COURSE - ANALYTICAL CHEMISTRY PRESENTED TO: SIR FAROOQUE

2. TOPIC ARITHMETIC MEAN

3. Arithmetic mean The arithmetic mean is what most people call the average. It is one of the simplest and most common ways to represent the central value of a group of numbers. 👉 Example: If you got marks 70, 80, and 90, the average (AM) tells us the "middle value" of your marks, which is 80.

4. Definition Arithmetic Mean is the value you get : when you add up all the numbers and then divide by how many numbers there are. Arithmetic mean(A.M)= sum of all value (ΣX) total no of value (N)

5. where do we use A.M?? 📊 Used in statistics to find central tendency. 📈 Used in economics (e.g., average income). 📚 Used in education (e.g., average marks of a student). ⚽ Used in sports (e.g., average runs, goals). 🏥 Used in health (e.g., average heart rate, blood pressure).

6. When data is given as simple numbers only (without frequency or groups), we call it an Individual Series. 👉 In this case, we just add all the numbers and divide by how many numbers there are. Types ✓ Individual series ✓Discrete series ✓Continueous series Individual series Arithmetic mean(A.M)= sum of all value (ΣX) total no of value (N)

7. Examples- ⚡Marks of students =10,20,30,40,50,60 Add : 10+20+30+40+50+60= 210 Count : = 6 Divide : 210÷6 =35 ✅A.M = 35 ⚡ Runs scored by a player= 12,15,18,20,25 Add : = 12+15+18+20+25= 90 Count : = 5 Divide : 90÷5=18 ✅A.M = 18

8. Discrete Series Discrete Series represent discrete variables with exact or finite values. Example: 20, 50 ,60 ,70, 80 No.of Students : 4, 8, 10, 15, 5. Calculate of arithmetic mean from discrete series. Example . Value (x), frequency (f). x. f. fx. 20. 4. 80 50. 8. 400. 60. 10. 600. 70. 15 1050 80. 5. 400. £fx= 80+400+600+1050+400=2530. £f=4+8+10+15+5= 42 2530/42 = 60.23.

9. Discrete Series Example:2 Marks= 40, 45, 63, 75, 80 , 90. No.of students: 5, 2, 7, 2, 7, 3 x. f. fx 40. 5. 200 45. 2 90 63. 7. 441 75. 2. 150 80. 7. 560 90. 3 270 £fx= 200+90+441+150+560+ 270 = 1711 £f= 5+2+7+2+7+3= 26 1711/26 = 65.80

10. Continueous series A continuous series is when data is presented in intervals ( not a single values) with their frequencies and the mid point of intervals are used to calculate the mean Example 1: Class interval:0-10,10-20,20-30 Frequency:4,6,10 Mid point:5,15,25 Fx:20,90,250 £fx:20+90+250=360 £f:4+6+10=20 Divide:360/20=18

11. Continueous series Example 2: Class interval= 0-20,20-40,40-60,60-80,80-100 Frequency: 5,8,12,10,5 Mid point; 10,30,50,70,90 Fx: 50,240,600,700,450 £fx:50+240+600+700+450=2040 £f:5+8+12+10+5=40 Divide:2040/40=51

12. Any Questions? THANK YOU