Statistics: Concepts, Formulas, and Clear Examples

Statistics MCQs cover mean, median, mode, range/variance light, and reading frequency tables. Mean uses all values; median resists outliers.

Grouped data: use class marks (midpoints) for approximate mean; median uses cumulative frequency.

Mode is the most frequent value; bimodal sets have two modes.

Mean, median, mode

Mean

$$\bar{x} = \frac{\sum x_i}{n}$$

Median (odd n)

$$\text{middle after sort}$$

Mode

$$\text{highest frequency value}$$

Example — Median even count

Sorted 3,5,8,10 → median = $(5+8)/2=6.5$.

Grouped mean

Assumed mean optional

$$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$

$x_i$ = class mark.

Median class

• Locate $\frac{N}{2}$ on cumulative frequency; median class where cum freq crosses N/2.

Range and deviation

Range

$$\max - \min$$

Variance (def)

$$\sigma^2 = \frac{\sum (x_i-\bar{x})^2}{n}$$

Change in data

• Adding constant to all data adds same to mean; median shifts same.
• Multiplying all by k multiplies mean and median by k.

Ogive and charts

• Less-than ogive: cum freq vs upper bound.
• Pie chart: angle = fraction × 360°.

Step-by-step method for exam questions

1. Identify raw vs grouped data.
2. Sort for median; tally freq for mode.
3. Compute mean from sum/count or Σfx/Σf.
4. For grouped median, find median class then interpolate if formula given.
5. Check effect of outliers on mean vs median.
6. Select option.

Formula cheat sheet

Frequently asked questions

Mean vs median skew?

Outliers pull mean; median more stable.

No unique mode?

Uniform data: no mode or all modes.

Class width unequal?

Still use marks; careful with histogram area interpretation.

Missing frequency?

Total freq minus known sums.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.