Statistics : SGT
STATISTICS
Collection and Representation of Data
| Tool | Purpose | Key Feature |
|---|---|---|
| Pictograph | Visual representation | Uses symbols/pictures |
| Tally Marks | Counting frequency | Group of five marks |
| Bar Graph | Data comparison | Equal width bars |
| Double Bar Graph | Compare two sets | Side-by-side bars |
| Pie Chart | Percentage view | Circle sectors (360°) |
Memory Tip: P – T – B – D – P → Pictograph, Tally, Bar, Double Bar, Pie
Exam Tip: Always check total frequency before drawing or interpreting any chart.
Graphical Representation of Data
| Graph Type | Used For | X-axis | Y-axis |
|---|---|---|---|
| Bar Graph | Discrete Data | Categories | Frequency |
| Histogram | Continuous Data | Class Intervals | Frequency |
| Frequency Polygon | Trend of Data | Class Marks | Frequency |
Memory Rule: Histogram = No gaps, Bar graph = Gaps allowed
Exam Tip: Convert class intervals into class marks while drawing frequency polygon.
Measures of Central Tendency (Ungrouped Data)
| Term | Formula / Method | Use Case |
|---|---|---|
| Mean | Sum of observations ÷ Number | Average value |
| Median | Middle value (after ordering) | Central value |
| Mode | Most repeated value | Most frequent item |
Memory Code: M³ = Mean, Median, Mode
Exam Tip: Always arrange values in ascending order before finding median.
Measures of Central Tendency (Grouped Data)
| Measure | Formula | Condition |
|---|---|---|
| Mean | ∑fx / ∑f | Step Deviation for large data |
| Median | L + ( (N/2 – cf) / f ) × h | Use cumulative frequency |
| Mode | L + ( (f₁ – f₀) / (2f₁ – f₀ – f₂) ) × h | Use modal class |
Formula Hint:
Median depends on N/2, Mode depends on highest frequency class.
Exam Tip: In grouped data, median class = class where cumulative frequency first exceeds N/2.