Complete Statistics Formulas for High School Students

FORMULA SHEET OF MATHEMATICS
𝑼𝒏𝒈𝒓𝒐𝒖𝒑𝒆𝒅 𝑫𝒂𝒕𝒂
1. 𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐴. 𝑀. ): 𝐴. 𝑀. = 𝛴𝑥 / 𝑛
2. 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐺. 𝑀. ): 𝐺. 𝑀. = ⁿ√(𝑥₁ × 𝑥₂ × 𝑥₃ × . . .× 𝑥ₙ)
𝑜𝑟 𝐺. 𝑀. = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝛴𝑙𝑜𝑔(𝑥) / 𝑛)
3. 𝐻𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐻. 𝑀. ): 𝐻. 𝑀. = 𝑛 / 𝛴(1/𝑥)
4. 𝑀𝑜𝑑𝑒: 𝑀𝑜𝑑𝑒 = 𝑇ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑡ℎ𝑎𝑡 𝑜𝑐𝑐𝑢𝑟𝑠 𝑚𝑜𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑙𝑦
5. 𝑀𝑒𝑑𝑖𝑎𝑛:
𝐼𝑓 𝑛 𝑖𝑠 𝑜𝑑𝑑: 𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑚𝑖𝑑𝑑𝑙𝑒 𝑣𝑎𝑙𝑢𝑒
𝐼𝑓 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛: 𝑀𝑒𝑑𝑖𝑎𝑛 = (𝑥ₙ/₂ + 𝑥₍ₙ/₂₊₁₎) / 2

𝑮𝒓𝒐𝒖𝒑𝒆𝒅 𝑫𝒂𝒕𝒂
1. 𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐴. 𝑀. ): 𝐴. 𝑀. = 𝛴𝑓𝑥 / 𝛴𝑓
2. 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐺. 𝑀. ): 𝐺. 𝑀. = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝛴𝑓 𝑙𝑜𝑔(𝑥) / 𝛴𝑓)
3. 𝐻𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑀𝑒𝑎𝑛 (𝐻. 𝑀. ): 𝐻. 𝑀. = 𝛴𝑓 / 𝛴(𝑓/𝑥)
4. 𝑀𝑜𝑑𝑒: 𝑀𝑜𝑑𝑒 = 𝐿 + [(𝑓₁ − 𝑓₀) / (2𝑓₁ − 𝑓₀ − 𝑓₂)] × ℎ
𝑊ℎ𝑒𝑟𝑒:
𝐿 = 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
𝑓₁ = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
𝑓₀ = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
𝑓₂ = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑎𝑓𝑡𝑒𝑟 𝑚𝑜𝑑𝑎𝑙 𝑐𝑙𝑎𝑠𝑠
ℎ = 𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ
5. 𝑀𝑒𝑑𝑖𝑎𝑛: 𝑀𝑒𝑑𝑖𝑎𝑛 = 𝐿 + [(𝑁/2 − 𝐹) / 𝑓] × ℎ
𝑊ℎ𝑒𝑟𝑒:
𝐿 = 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠
𝑁 = 𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝐹 = 𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠
ℎ = 𝑐𝑙𝑎𝑠𝑠 𝑤𝑖𝑑𝑡ℎ

𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒔 𝒐𝒇 𝑫𝒊𝒔𝒑𝒆𝒓𝒔𝒊𝒐𝒏
1. 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝑈𝑛𝑔𝑟𝑜𝑢𝑝𝑒𝑑 𝐷𝑎𝑡𝑎): 𝜎 = √[𝛴(𝑥 − 𝑥)² / 𝑛]
2. 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝐺𝑟𝑜𝑢𝑝𝑒𝑑 𝐷𝑎𝑡𝑎): 𝜎 = √[𝛴𝑓(𝑥 − 𝑥)² / 𝛴𝑓]
3. 𝑀𝑒𝑎𝑛 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝑈𝑛𝑔𝑟𝑜𝑢𝑝𝑒𝑑 𝐷𝑎𝑡𝑎): 𝑀. 𝐷. = 𝛴|𝑥 − 𝑥| / 𝑛
4. 𝑀𝑒𝑎𝑛 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝐺𝑟𝑜𝑢𝑝𝑒𝑑 𝐷𝑎𝑡𝑎): 𝑀. 𝐷. = 𝛴𝑓|𝑥 − 𝑥| / 𝛴𝑓
5. 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒: 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎²

𝑴𝒂𝒕𝒓𝒊𝒄𝒆𝒔
Adj (A)
1. A-1 = ‖A‖
2. A = X-1B
3. Generalize Metrix Form
𝑎 𝑏 𝑥 𝑎𝑛𝑦 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑣𝑎𝑙𝑢𝑒
[ ] [y] = [ ]
c d any constant value

𝑻𝒓𝒊𝒈𝒏𝒐𝒎𝒆𝒕𝒓𝒊𝒄

1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
3. 1 + cot²θ = cosec²θ
4. sin θ = 1 / cosec θ
5. cos θ = 1 / sec θ
6. tan θ = 1 / cot θ
7. cosec θ = 1 / sin θ
8. sec θ = 1 / cos θ
9. cot θ = 1 / tan θ
10. tan θ = sin θ / cos θ
11. cot θ = cos θ / sin θ
12. • sin θ = P / H (Sine = Perpendicular ÷ Hypotenuse)