Stats (unit 1)

Statistics

The science of collecting, analyzing, interpreting, and presenting data

Primary Data

Data collected directly by the investigator for the first time

Secondary Data

Data collected by someone else and used by the investigator

Population

The complete set of items that data can be collected from

Sample A subset of the population selected for analysis

Variable A characteristic or attribute that can assume different values

Discrete Variable Takes specific, separate values (e.g. number of students)

Continuous Variable Can take any value within a range (e.g. height, weight)

Classification The process of arranging data into groups or classes

Tabulation Systematic arrangement of data in rows and columns

Frequency The number of times a particular value occurs in a dataset

Cumulative Frequency The total frequency accumulated up to a certain point

Central Tendency A central or typical value for a dataset (like mean, median, mode)

Mean (Ungrouped Data) Arithmetic Mean = (Sum of all values) / (Number of values)

Mean (Grouped Data) Arithmetic Mean = Σfx / Σf

Median (Ungrouped Data) Middle value when data is arranged in ascending order

Median (Grouped Data) Median = l + [(N/2 – F) / f] × h

Mode (Grouped Data) Mode = l + [(f1 – f0) / (2f1 – f0 – f2)] × h

Range Difference between the maximum and minimum values

Standard Deviation Measure of dispersion: SD = √(Σ(x – x̄)² / n)

Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100

Quartiles Values that divide data into four equal parts

Percentiles Divide the dataset into 100 equal parts

Deciles Divide the dataset into 10 equal parts

Ogive A graph of cumulative frequency

Histogram Bar graph used for frequency distribution of continuous data

Bar Diagram Used to represent discrete data using bars

Pie Chart Circular chart divided into sectors representing proportions

When to use Arithmetic Mean When data is quantitative and there's no extreme values

When to use Median When data has extreme values or is skewed

When to use Mode When data is categorical or the most frequent value is required

Grouped Frequency Table Used when data is large and continuous

Ungrouped Frequency Table Used when data is small and discrete