B
Biggan.me
Science & Math Calculators
🌐বাংলা
General Mathematics (SSC Classes 9-10)NCTB SSC General Math (Classes 9-10)Grouped StatisticsTrigonometric HeightsAlgebraic Expressions

SSC General Mathematics Solver & Equation Engine

Complete procedural equation solver for NCTB SSC General Mathematics (Classes 9-10). Grouped statistics (Mean, Median, Mode), trigonometry, algebra, and mensuration.

CalculatorFormulasExemplarsCasio fx-991ApplicationsFAQ

📊 Grouped Data Statistics: Mean, Median & Mode

Complete step-deviation table and analytical CQ formulas

Class Intervals & Frequencies:
Class #1
Class #2
Class #3
Grouped Frequency HistogramPeak Frequency: 8
431-40641-50851-60
NCTB Grouped Analysis Table:
Class IntervalMidpoint (xi)Freq (fi)Cum Freq (Fc)Step Dev (ui)fi × ui
31 – 4035.544-1-4
41 – 5045.561000
51 – 6055.581818
Total:n = 18--∑(fi·ui) = 4
Arithmetic Mean47.7222x̄ = a + (∑fi·ui / n) × h
Median49.3333Median Class: 41-50
Mode53Modal Class: 51-60
Step-by-Step Derivations (KaTeX):
Step-Deviation Arithmetic Mean
xˉ=a+(∑fiuin)×h\bar{x} = a + \left(\frac{\sum f_i u_i}{n}\right) \times h

অনুমিত গড় a = 45.5, \sum f_i u_i = 4, n = 18, শ্রেণি ব্যাপ্তি h = 10। \bar{x} = 45.5 + \left(\frac{4}{18}\right) \times 10 = 47.7222।

Median Class Determination & Formula
Median=L+(n2−Fcfm)×h\text{Median} = L + \left(\frac{\frac{n}{2} - F_c}{f_m}\right) \times h

n/2 = 9। সুতরাং মধ্যক শ্রেণি হলো 41 - 50 (যেখানে প্রথম ক্রমযোজিত গণসংখ্যা ≥ 9)। L = 41, F_c = 4, f_m = 6, h = 10। মধ্যক = 49.3333।

Modal Class & Formula
Mode=L+(f1f1+f2)×h\text{Mode} = L + \left(\frac{f_1}{f_1 + f_2}\right) \times h

সর্বোচ্চ গণসংখ্যা 8 বিদ্যমান 51 - 60 শ্রেণিতে। f_1 = 8 - 6 = 2, f_2 = 8 - 0 = 8। প্রচুরক = 51 + \left(\frac{2}{2 + 8}\right) \times 10 = 53.0000।

Scroll down to review Casio fx-991ES PLUS and fx-991EX ClassWiz hardware keystrokes.
STAT • TABLE • EQN
Active Result:
Mean: 47.7222 | Med: 49.3333

Formula & Derivation

Theoretical foundation, dimensional analysis, and governing boundary conditions.

NCTB General Mathematics Mathematical Foundations

The SSC General Mathematics curriculum emphasizes both algorithmic manipulation and analytical deduction across 7 major thematic domains. This procedural utility provides full algebraic proofs and step-by-step substitutions.

Chapter 17 (Statistics Formulas):

• Mean: x̄ = a + (∑fi·ui / n) × h

• Median: L + [(n/2 - Fc) / fm] × h

• Mode: L + [f1 / (f1 + f2)] × h

Chapter 10 (Heights & Distances):

• Single Elevation: h = d × tan(θ)

• Two Points: h = d / (cot θ1 - cot θ2)

• Broken Tree: x = [H sin θ] / [1 + sin θ]

Solved Textbook Examples

Three fully worked pedagogical exemplars: standard textbook, advanced edge-case, and authentic past board examination.

Board Exam Standard (CQ Part C — Grouped Statistics)bg-cyan-500/10 text-cyan-400 border border-cyan-500/20
Given the frequency distribution: 31-40 (f=4), 41-50 (f=6), 51-60 (f=8). Calculate the Mean using step-deviation and find the Mode.
Given Parameters:
  • Classes: 31-40 (4), 41-50 (6), 51-60 (8)
  • Total observations n = 18
  • Class width h = 10
Procedural Solution:
Assumed mean a = 45.5 (midpoint of 41-50).
Step-deviations: u1 = -1, u2 = 0, u3 = 1. Sum of fi·ui = (4 × -1) + (6 × 0) + (8 × 1) = 4.
Mean: x̄ = a + (∑fi·ui / n) × h = 45.5 + (4 / 18) × 10 = 47.72.
Modal class is 51-60 (highest freq 8). f1 = 8 - 6 = 2, f2 = 8 - 0 = 8.
Mode: L + [f1 / (f1 + f2)] × h = 51 + [2 / (2 + 8)] × 10 = 53.00.
Final Answer:Mean = 47.72 and Mode = 53.00.
Board Exam Standard (CQ Part C — Trigonometric Heights)bg-emerald-500/10 text-emerald-400 border border-emerald-500/20
From a point on the ground 30 meters away from the base of a tower, the angle of elevation to the top is 60°. Calculate the height of the tower.
Given Parameters:
  • Horizontal distance d = 30 m
  • Angle of elevation θ = 60°
Procedural Solution:
In the right triangle formed: tan(θ) = Opposite / Adjacent = h / d.
tan(60°) = h / 30
√3 = h / 30 ⟹ h = 30√3 = 30 × 1.73205 = 51.9615 meters.
Final Answer:Height of the tower is 51.9615 meters (approx).
Algebraic Identities (CQ Part B — Value Determination)bg-purple-500/10 text-purple-400 border border-purple-500/20
If a + b = 5 and ab = 6, find the values of a² + b² and a³ + b³.
Given Parameters:
  • a + b = 5
  • ab = 6
Procedural Solution:
a² + b² = (a + b)² - 2ab = (5)² - 2(6) = 25 - 12 = 13.
a³ + b³ = (a + b)³ - 3ab(a + b) = (5)³ - 3(6)(5) = 125 - 90 = 35.
Final Answer:a² + b² = 13 and a³ + b³ = 35.

Casio Scientific Calculator Keystroke GuideExam Ready

Exact button sequences permitted in board and university entrance examination halls:

Casio fx-991ES PLUS / 2nd Edition
Board standard grouped data analysis.
1. Enable Frequency Table
SHIFTMODE▼4 (STAT)1 (ON)
Shows Freq column.
2. Enter Data in STAT Mode
MODE3 (STAT)1 (1-VAR)[Fill X & FREQ]AC
Always press AC after data entry to store in memory.
3. Read Mean (x̄)
SHIFT1 (STAT)4 (Var)2 (x̄)=
Displays the exact arithmetic mean.

Practical Applications

How this scientific principle drives chemical engineering, aerospace, medicine, and research.

Trigonometric height calculations serve as the foundation of surveying, architecture, and geodesy. Step-deviation grouped statistics form the standard protocol in demographic census analysis, market research, and industrial quality control.

Frequently Asked Questions

Answers to common conceptual misconceptions and board examination guidelines.

How are boundary frequencies f1 and f2 evaluated for Mode calculation?▼
The modal class contains the maximum frequency (fm). f1 is the difference between modal frequency and preceding class frequency (f1 = fm - f(m-1)). f2 is the difference between modal frequency and succeeding class frequency (f2 = fm - f(m+1)). If the modal class is the first interval, f(m-1) = 0; if it is the last interval, f(m+1) = 0.
What is the governing equation for the classic Broken Tree problem?▼
When a tree of total height H breaks at height x and touches the ground making angle θ with the ground: sin(θ) = x / (H - x). Solving for x gives x = [H × sin(θ)] / [1 + sin(θ)].
How do Casio fx-991ES PLUS and fx-991EX ClassWiz solve grouped statistics?▼
On fx-991EX ClassWiz: Menu > 6 (Statistics) > 1 (1-Variable) with Frequency ON (Shift > Menu > Statistics > On). Enter class midpoints in X and frequencies in Freq, then press OPTN > 2 (1-Variable Calc) to view x̄, ∑x, and n. On fx-991ES PLUS: Mode > 3 (STAT) with Frequency enabled via Shift > Mode > Down > Stat > 1.