HSSLIVE Plus One Maths Chapter 15: Statistics Notes

Statistics provides methods for collecting, organizing, analyzing, and interpreting data to make informed decisions. This chapter covers measures of central tendency, dispersion, correlation, and basic probability distributions. Students will learn to summarize data effectively, identify patterns, and draw valid conclusions despite variability and uncertainty. These analytical skills are increasingly important in our data-driven world, with applications in research, business analytics, public policy, healthcare, and virtually every field that relies on evidence-based decision making.

Chapter 15: Statistics

Basic Terminology:

• Population: The entire collection of items under study
• Sample: A subset of the population
• Variable: A characteristic that can take different values
• Frequency: Number of times a value occurs

Data Representation:

1. Tabular Form: Frequency distribution table
2. Graphical Form: Histogram, frequency polygon, ogive

Measures of Central Tendency:

1. Mean:
   • For ungrouped data: x̄ = Σxi/n
   • For grouped data: x̄ = Σfixi/Σfi
2. Median: Middle value when data is arranged in order
   • For grouped data: Median = l + [(n/2 – cf)/f] × h where l is lower limit, cf is cumulative frequency before median class, f is frequency of median class, h is class width
3. Mode: Value that occurs most frequently
   • For grouped data: Mode = l + [(f1 – f0)/(2f1 – f0 – f2)] × h where f1 is frequency of modal class, f0 is frequency of preceding class, f2 is frequency of succeeding class

Measures of Dispersion:

1. Range: Difference between maximum and minimum values
2. Mean Deviation: Average of absolute deviations from mean
3. Variance: Average of squared deviations from mean
4. Standard Deviation: Square root of variance
   • For ungrouped data: σ = √[Σ(xi – x̄)²/n]
   • For grouped data: σ = √[Σfi(xi – x̄)²/Σfi]

Correlation:

Measures the degree and direction of relationship between two variables.

• Karl Pearson’s Coefficient of Correlation: r = Σ(xi – x̄)(yi – ȳ)/√[Σ(xi – x̄)² × Σ(yi – ȳ)²]
• Properties:
  • -1 ≤ r ≤ 1
  • r = 1: perfect positive correlation
  • r = -1: perfect negative correlation
  • r = 0: no correlation