Concept 10 of 10Foundation

📌 Formula Sheet — Data Handling

Statistics formulas with the thinking behind each.

Mean (average) = (Sum of values) / (Number of values)

Means: the 'even share' if total were split equallyUse when: summarizing a set of numeric values

Why: Imagine pooling everyone's share into one heap, then redistributing equally. Each person gets the total ÷ count.

⚠ Trap: Mean is pulled by extreme values. One outlier can move it a lot.

Sum = Mean × Number of values

Means: rearrangement of the mean formulaUse when: you know the mean and count, need total (or find a missing value)

Why: If each "share" = mean, and there are n shares, total = n × mean.

⚠ Trap: Use this when a problem says "mean of N numbers is X, one is missing" — compute total and subtract.

Median = middle value when data is SORTED

If n is odd: median = (n+1)/2 th valueIf n is even: median = average of the n/2 and (n/2)+1 th values

Why: Median splits the data into two equal halves. It's robust — doesn't care about size of extreme values, only their position.

⚠ Trap: You MUST sort the data first. Unsorted data gives a wrong 'median'.

Mode = most frequent value

Means: highest frequency in the tallyUse when: 'most popular' — shoe sizes, favourite colour

Why: Mode spots the typical choice without caring about numeric size. Great for categorical data.

⚠ Trap: Data can have 0, 1, or many modes. If everything is unique, there's no mode.

Range = Maximum − Minimum

Means: spread of the dataUse when: summarising variability

Why: It measures the gap between the two extremes — a rough sense of how spread out the data is.

⚠ Trap: Range is super sensitive to outliers. A single strange value can blow it up.

Pie chart: slice angle = (category value / total) × 360°

Means: convert each category's share into degreesUse when: drawing or reading a pie chart

Why: A full circle = 360°. Each category gets a fraction of that, proportional to its share of the total.

⚠ Trap: All slice angles MUST sum to 360°. If they don't, you've miscounted or miscomputed.

Pictograph: value = (number of icons) × (icon-scale)

Means: read the legend ("1 icon = k units"), then multiplyUse when: interpreting pictographs

Why: Each icon is a shorthand for a fixed amount. Half an icon = half that amount.

⚠ Trap: Always read the LEGEND first. Two charts may use different scales.

💡 Tip:Mean, median, and mode all try to describe a 'typical' value — but pick the right one based on what you're studying.