Applied Statistics — BMS | Complete Notes with Full Solutions
Applied Statistics
Complete BMS Notes — Detailed Solutions
AM · GM · HM · Median · Quartile · Decile · Percentile · Mode · Range · QD · MD
Part 1 — Arithmetic Mean (AM)
Formula Card
AM — Solved Examples
Ungrouped Data
Example 1 — Find AM of: 10, 20, 30, 40, 50
Given: x = 10, 20, 30, 40, 50
To find: Arithmetic Mean (AM)
Formula: AM = Σx / n
Step 1 — Add all values
Σx = 10 + 20 + 30 + 40 + 50 = 150
Page 1 | Applied Statistics | BMS
,Applied Statistics — BMS | Complete Notes with Full Solutions
Step 2 — Count values
n = 5
Step 3 — Apply formula
AM = Σx
──────
n
AM = = 30
∴ AM = 30
Example 2 — Find AM of marks: 45, 62, 78, 55, 80, 40, 95
Given: x = 45, 62, 78, 55, 80, 40, 95
To find: Arithmetic Mean (AM)
Formula: AM = Σx / n
Step 1 — Add all values
Σx = 45 + 62 + 78 + 55 + 80 + 40 + 95 = 455
Step 2 — Count values
n = 7
Step 3 — Apply formula
AM = Σx
──────
n
AM = = 65
∴ AM = 65 marks
Page 2 | Applied Statistics | BMS
,Applied Statistics — BMS | Complete Notes with Full Solutions
Grouped Data — Simple Frequency Table
Example 4 — Find AM
x = 10, 20, 30, 40 | f = 3, 5, 8, 4
Formula: AM = Σfx / N
Step 1 — Build the fx column
x f fx —
10 3 30
20 5 100
30 8 240
40 4 160
Total N = 20 Σfx = 530
Step 2 — Apply formula
AM = Σfx
───────
N
AM = = 26.5
∴ AM = 26.5
Example 5 — Class Intervals
Given: Frequency distribution with class intervals
To find: Arithmetic Mean (AM)
Formula: AM = Σfx / N
Step 1 — Find midpoint (x) of each class
Midpoint = (Lower limit + Upper limit) / 2
0–10 → 5 | 10–20 → 15 | 20–30 → 25 | 30–40 → 35 | 40–50 → 45
Step 2 — Build the full table
Page 3 | Applied Statistics | BMS
, Applied Statistics — BMS | Complete Notes with Full Solutions
Class Midpoint (x) f fx —
0–10 5 5 25
10–20 15 8 120
20–30 25 12 300
30–40 35 10 350
40–50 45 5 225
Total — N = 40 Σfx = 1020
Step 3 — Apply formula
AM = Σfx
───────
N
AM = = 25.5
∴ AM = 25.5 marks
Page 4 | Applied Statistics | BMS
Applied Statistics
Complete BMS Notes — Detailed Solutions
AM · GM · HM · Median · Quartile · Decile · Percentile · Mode · Range · QD · MD
Part 1 — Arithmetic Mean (AM)
Formula Card
AM — Solved Examples
Ungrouped Data
Example 1 — Find AM of: 10, 20, 30, 40, 50
Given: x = 10, 20, 30, 40, 50
To find: Arithmetic Mean (AM)
Formula: AM = Σx / n
Step 1 — Add all values
Σx = 10 + 20 + 30 + 40 + 50 = 150
Page 1 | Applied Statistics | BMS
,Applied Statistics — BMS | Complete Notes with Full Solutions
Step 2 — Count values
n = 5
Step 3 — Apply formula
AM = Σx
──────
n
AM = = 30
∴ AM = 30
Example 2 — Find AM of marks: 45, 62, 78, 55, 80, 40, 95
Given: x = 45, 62, 78, 55, 80, 40, 95
To find: Arithmetic Mean (AM)
Formula: AM = Σx / n
Step 1 — Add all values
Σx = 45 + 62 + 78 + 55 + 80 + 40 + 95 = 455
Step 2 — Count values
n = 7
Step 3 — Apply formula
AM = Σx
──────
n
AM = = 65
∴ AM = 65 marks
Page 2 | Applied Statistics | BMS
,Applied Statistics — BMS | Complete Notes with Full Solutions
Grouped Data — Simple Frequency Table
Example 4 — Find AM
x = 10, 20, 30, 40 | f = 3, 5, 8, 4
Formula: AM = Σfx / N
Step 1 — Build the fx column
x f fx —
10 3 30
20 5 100
30 8 240
40 4 160
Total N = 20 Σfx = 530
Step 2 — Apply formula
AM = Σfx
───────
N
AM = = 26.5
∴ AM = 26.5
Example 5 — Class Intervals
Given: Frequency distribution with class intervals
To find: Arithmetic Mean (AM)
Formula: AM = Σfx / N
Step 1 — Find midpoint (x) of each class
Midpoint = (Lower limit + Upper limit) / 2
0–10 → 5 | 10–20 → 15 | 20–30 → 25 | 30–40 → 35 | 40–50 → 45
Step 2 — Build the full table
Page 3 | Applied Statistics | BMS
, Applied Statistics — BMS | Complete Notes with Full Solutions
Class Midpoint (x) f fx —
0–10 5 5 25
10–20 15 8 120
20–30 25 12 300
30–40 35 10 350
40–50 45 5 225
Total — N = 40 Σfx = 1020
Step 3 — Apply formula
AM = Σfx
───────
N
AM = = 25.5
∴ AM = 25.5 marks
Page 4 | Applied Statistics | BMS
