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📊 Statistics — Complete In-Depth Notes (From Your PDF)

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UNIT 1: MEASURES OF CENTRAL TENDENCY

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1. Arithmetic Mean (AM) — Simple Average

• Add up all values, divide by how many there are.
• Example: Data = 2, 3, 6, 7, 8, 11, 6 → Sum = 43, n = 7 → Mean = 43/7 ≈ 6.14

• Multiply each class mark (midpoint) by its frequency, sum all of those, divide by total frequency.

• Each value gets a "weight" (importance). Multiply each value by its weight, sum, divide by sum of weights.
• Example from your notes: X₁=5, X₂=4, X₃=2 with weights W₁=5, W₂=4, W₃=3: $$\bar{X}_w = \frac{(5)(5)+(4)(4)+(2)(3)}{5+4+3} = \frac{25+16+6}{12} = \frac{47}{12}$$

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2. Geometric Mean (GM)

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3. Harmonic Mean (HM)

Key relationship: HM = Reciprocal of the Arithmetic Mean of reciprocals. Also: HM = 1 / AM of (1/x).

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Key Relationship Between AM, GM, HM

• The arithmetic mean is always ≥ geometric mean, which is always ≥ harmonic mean (for positive values).
• Also: GM² = AM × HM (the geometric mean squared equals AM times HM).

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4. Median

• Arrange data in ascending order.
• If n is odd: Median = middle value = value at position (n+1)/2
• If n is even: Median = average of the two middle values

• L = lower boundary of median class
• h = class interval width
• n = total frequency
• F = cumulative frequency before median class
• f = frequency of median class

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5. Mode

• L = lower boundary of modal class (class with highest frequency)
• f₁ = frequency of modal class
• f₀ = frequency of class before modal class
• f₂ = frequency of class after modal class
• h = class width

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Relationship Between Mean, Median, Mode

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Advantages of Arithmetic Mean

• Uses all data values
• Easy to calculate
• Suitable for further algebraic operations

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UNIT 2: MEASURES OF DISPERSION

Think of it this way: Two classes both have a mean score of 60. But Class A has scores 58, 59, 60, 61, 62 (low dispersion) while Class B has 20, 40, 60, 80, 100 (high dispersion). Same mean — very different spread.

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1. Range

• Class mark = (Upper boundary + Lower boundary) / 2 = midpoint of a class

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2. Quartile Deviation (QD) / Semi-Interquartile Range

• Q1 = 25th percentile (lower quartile)
• Q2 = 50th percentile = Median
• Q3 = 75th percentile (upper quartile)

• Median = 40
• Lower half: 10, 20, 30 → Q1 = 20
• Upper half: 50, 60, 70 → Q3 = 60
• QD = (60 - 20) / 2 = 20

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3. Mean Deviation (MD) / Average Deviation

• Mean = 34.5
• MD about mean = Σ|x - 34.5| / n
• MD about median: Find median first using formula, then compute |x - median|

The key: Always take the absolute value | | so negative deviations don't cancel out positive ones.

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4. Standard Deviation (SD) — Most Important

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Summary: Absolute vs Relative Measures of Dispersion

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UNIT 3: SKEWNESS

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UNIT 4: PROBABILITY

Basic Concepts

• Experiment: Any action with an uncertain outcome (rolling a die, flipping a coin).
• Sample Space (S): The set of ALL possible outcomes.
  • Roll a die: S = {1, 2, 3, 4, 5, 6}
  • Flip a coin: S = {Head, Tail}
  • Roll two dice: S has 6 × 6 = 36 sample points
• Sample Point: A single possible outcome (e.g., getting a "3" when rolling a die).
• Event: A subset of the sample space (e.g., getting an even number).

Types of Events

Probability Formula

• Probability of Head in a coin flip = 1/2 = 50%
• Rolling a die: probability of getting 4 = 1/6
• Probability of getting no particular number (equal chance): 1/6 each

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UNIT 5: COUNTING TECHNIQUES

The Multiplication Rule (Fundamental Counting Principle)

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Permutations (Order Matters)

• n = total objects, r = objects being arranged
• Example: How many ways to arrange 3 letters from {A, B, C, D}? P(4,3) = 4!/(4-3)! = 4!/1! = 24

• Example from your notes: "COLUMNS" → 7 letters, some may repeat Count repeated letters first, then apply formula.

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Combinations (Order Does NOT Matter)

• C(10, 2) = 10!/(2! × 8!) = 45

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MCQ-Style Class Intervals Tip (from your notes)

• Class width (h) = 27 − 18 = 9 → but true class boundaries adjust by 0.5:
  • 17.5–26.5, 26.5–35.5, 35.5–44.5
  • True h = 9
• Class mark (midpoint) = (Lower boundary + Upper boundary) / 2
  • Example: class (−2.5) to (4): class mark = (−2.5 + 4)/2 = 0.75

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Quick Reference: Key Formulas Summary

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How to Remember All of This

1. Central Tendency: AM = everyday average. GM = for growth/speed. HM = for rates going back and forth.
2. Dispersion: Range = quick & rough. SD = most precise. MD = simple absolute deviations.
3. Skewness: If mean > mode → data is stretched to the right (positive skew).
4. Probability: Count what you want ÷ count everything possible.
5. Counting: Order matters → Permutation. Order doesn't matter → Combination.

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💉 Anti-Diabetic Drugs — Simplest Complete Notes

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🔑 FIRST: What is Diabetes?

Simple Definition: Your blood sugar stays too high for too long because insulin isn't working properly.

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🔑 THREE TYPES OF DIABETES — Easy to Remember

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🔑 SYMPTOMS OF DIABETES — "The 3 P's + More"

• Polyuria — peeing too much
• Polydipsia — drinking too much (thirst)
• Polyphagia — eating too much (hunger)

• Weight loss
• Blurred vision
• Smell of acetone on breath
• Nausea, vomiting
• Kussmaul breathing (deep, fast breathing — in severe cases)
• Lethargy, stupor

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🔑 COMPLICATIONS (Long-term damage from uncontrolled diabetes)

"NERVE-KIDNEY-EYE-HEART-FEET"

• Heart disease & hypertension
• Diabetic eye disease (retinopathy, cataracts)
• Renal (kidney) disease
• Neuropathy (nerve damage)
• Peripheral vascular disease & foot problems

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🔑 TREATMENT OVERVIEW

Diabetes Treatment
       ├── 1. INSULIN (injections)
       └── 2. ORAL HYPOGLYCEMIC AGENTS (pills)

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PART 1: INSULIN 💉

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How Does Insulin Work? (Mechanism of Action)

Step 1: Insulin attaches to receptor (α-subunit) on cell surface
       ↓
Step 2: Receptor activates itself (β-subunit phosphorylates → IRS activated)
       ↓
Step 3: Two pathways triggered:
   → PI3 Kinase pathway: moves GLUT-4 transporters to surface → sugar enters cell
   → MAP Kinase pathway: tells cell to grow & divide

• ✅ Glucose uptake by cells ↑
• ✅ Glycogen synthesis ↑ (stores sugar)
• ✅ Glycolysis ↑ (burns sugar)
• ✅ Triglyceride synthesis ↑
• ✅ Blood glucose ↓

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Types of Insulin — "From Fastest to Slowest"

Memory trick: Think of a race — some insulins are sprinters, some are marathon runners.

Key Details to Remember:

• Fastest absorption, shortest action
• Lispro = proline at B28 swapped for lysine
• Aspart = proline at B28 swapped for aspartic acid
• Glulisine = glutamic acid replaces lysine at B29
• Reduces hypoglycemia by 20–30%

• Only insulin that can be given IV (used in emergencies)
• Used in: diabetic ketoacidosis (DKA), diabetic coma, acute infections, post-surgery

• = Insulin + Protamine (ratio 6:1 molecules)
• Can be mixed with regular insulin
• Given twice daily

• 30% Semilente + 70% Ultra-lente mix

• Delayed onset, long duration
• Given once daily with regular insulin

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Routes of Insulin Administration

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Uses of Insulin

1. Type 1 DM (mandatory — no choice)
2. Type 2 DM (when oral drugs fail)

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Complications / Side Effects of Insulin

1. Hypoglycemia (LOW BLOOD SUGAR) — Most Important ⚠️

• Too high a dose
• Delayed meal
• Unusual exercise
• More common with human insulin

• 🧠 Mental confusion, headache, inability to concentrate
• 👁️ Disturbed speech & vision
• 💓 Tachycardia, palpitations
• 💦 Sweating, tremors
• 🤤 Hunger
• ⚡ Convulsions & coma (severe)

2. Other Side Effects:

• Lipodystrophy (fat changes at injection site)
• Insulin resistance
• Allergic reactions

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Drug Interactions with Insulin

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PART 2: ORAL HYPOGLYCEMIC AGENTS (OHAs) 💊

These are pills taken by mouth — used mainly in Type 2 DM

Oral Anti-Diabetics
    ├── SECRETAGOGUES (make pancreas release more insulin)
    │       ├── Sulfonylureas
    │       └── Meglitinides
    └── SENSITIZERS (make cells more sensitive to insulin)
            ├── Biguanides
            ├── Thiazolidinediones (Glitazones)
            └── Alpha-Glucosidase Inhibitors

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1. SULFONYLUREAS 🏆 (Most Classic Oral Drug)

How they work (MOA):

"They force the pancreas to release insulin by closing K⁺ channels"

Sulfonylurea binds to receptor on β-cell
       ↓
K⁺ channel CLOSES → Cell membrane depolarizes
       ↓
Ca²⁺ channel OPENS → Ca²⁺ enters cell
       ↓
Insulin granules released → Blood sugar ↓

• ↑ Number of insulin receptors (up-regulation)
• ↑ Binding of insulin to receptors
• ↑ Effect of insulin
• ↓ Serum glucagon

Generations:

Individual Drug Profiles (Quick Cards):

Pharmacokinetics (general for all SUs):

• Well absorbed orally
• Peak effect: 2–4 hours
• Highly protein-bound → drug interactions
• Excreted by kidneys → careful in elderly & renal insufficiency

Uses:

1. Type 2 DM (NIDDM)
2. Combined with insulin to reduce insulin dose

Adverse Effects — "HGPAW + Blood":

• Hypoglycemia (most important)
• GIT — nausea, vomiting, diarrhea
• Photosensitivity
• Allergic reactions (rashes)
• Weight gain (↑ appetite)
• Blood dyscrasias — leukopenia, thrombocytopenia, agranulocytosis, hemolytic anemia

Contraindications:

• Hypersensitivity
• Renal/hepatic/endocrine dysfunction
• Pregnancy ❌

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2. MEGLITINIDES (Repaglinide, Nateglinide)

"Mini sulfonylureas — works only around meal time"

• Rapid onset + short duration → acts at mealtime
• Called "postprandial glucose regulators"
• Should NOT be combined with sulfonylureas (overlap)
• Can combine with metformin or glitazones

• Take 1–30 minutes before meals
• Metabolized by CYP3A4 in liver
• Excreted through bile

• Hypoglycemia (less than sulfonylureas)
• Weight gain

• CYP3A4 inhibitors (ketoconazole, erythromycin, clarithromycin) → enhance effect → risk of hypoglycemia
• CYP3A4 inducers (rifampin, carbamazepine, barbiturates) → reduce effect

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3. BIGUANIDES (Metformin — King of Type 2 DM) 👑

"Metformin doesn't make more insulin — it just uses what's there better"

• ↓ Hepatic gluconeogenesis (liver stops making new sugar) — Main effect
• ↑ Glycolysis in peripheral tissues (burns sugar faster)
• ↓ Glucose absorption from gut
• ↓ Plasma glucagon
• ↑ Binding of insulin to its receptors

• Type 2 DM (especially with obesity)
• Refractory obesity with hyperglycemia

• Metallic taste in mouth
• Anorexia, nausea, vomiting
• Lactic acidosis (rare but serious — especially with phenformin)

• Renal disease
• Hepatic disease
• Alcoholism
• Chronic cardiopulmonary dysfunction

Why? These conditions risk lactic acidosis.

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4. THIAZOLIDINEDIONES / GLITAZONES (Pioglitazone, Rosiglitazone)

"They target fat cells to make the whole body more sensitive to insulin"

• Activate PPAR-γ (a receptor inside cell nucleus)
• This regulates adipocyte production, fatty acid secretion, and glucose metabolism
• Result: ↑ Insulin sensitivity in fat, liver, and muscle

• Weight gain
• Fluid retention / edema
• Liver toxicity (especially troglitazone — withdrawn)
• Increased risk of heart failure (rosiglitazone)

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5. ALPHA-GLUCOSIDASE INHIBITORS (Acarbose, Miglitol)

"They block sugar digestion in the gut — sugar absorbed slower"

• Inhibit alpha-glucosidase enzyme in the intestine
• Slows breakdown of complex carbohydrates → slower glucose absorption → blunts after-meal spike

• Flatulence (gas), bloating, diarrhea (undigested carbs ferment in gut)

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🧠 MASTER MEMORY TABLE — Oral Anti-Diabetics at a Glance

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⚡ RAPID RECALL — Insulin Types in Order

ULTRA-FAST → SHORT → INTERMEDIATE → LONG
  Lispro      Regular    NPH/Lente     Glargine
  Aspart      (IV only)  (twice daily)  (once daily)
  Glulisine

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⚡ ONE-LINE MEMORY TRICKS