Statistics Flashcards

The process of selecting a subset of individuals or items from a population to represent the whole population.

The entire group of individuals or items that data could be collected from.

A subset of the population chosen for data collection.

A sampling method where every member of the population has an equal chance of being selected.

A sampling method where members are selected at regular intervals from an ordered list.

A sampling method where the population is divided into groups (strata) and a proportional sample is taken from each group.

A sampling method where researchers select a sample that reflects certain characteristics of the population.

Occurs when the sample does not accurately represent the population, leading to misleading results.

The number of individuals or items included in the sample.

Data that is descriptive and non-numerical, such as colours or opinions.

Data that is numerical and can be measured, such as height or temperature.

Quantitative data that can only take specific values, such as the number of people.

Quantitative data that can take any value within a range, such as weight or time.

Data collected directly by the researcher for a specific purpose.

Data that has been collected by someone else and is used by the researcher.

A graph that uses bars to show frequencies or values for different categories.

A circular chart divided into sectors, showing proportions of a whole.

A graph showing frequencies of continuous data, with bars representing intervals.

A graph showing the relationship between two variables using plotted points.

A graph that uses lines to show trends or changes over time.

A way of organising numerical data to show its distribution.

A graph that connects the midpoints of histogram bars with straight lines.

A graph showing the running total of frequencies, used to find medians and quartiles.

Mean = Sum of values ÷ Number of values.

Median position = (n + 1) ÷ 2, where n is the number of values.

Range = Largest value - Smallest value.

IQR = Upper quartile - Lower quartile.

Frequency density = Frequency ÷ Class width (used in histograms).

Estimated mean = (Σfx) ÷ Σf, where f is frequency and x is midpoint.

Standard deviation = √(Σ(x - mean)² ÷ n), where x is each value and n is the number of values.

A data value that is significantly different from the rest of the data set.

Outliers are values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR.

Outliers can affect measures of central tendency and spread, such as the mean and range.

A graph showing the relationship between two variables using plotted points.

A relationship where as one variable increases, the other also increases.

A relationship where as one variable increases, the other decreases.

No apparent relationship between the two variables.

A straight line drawn on a scatter diagram to show the general trend of the data.

Estimating values within the range of the data using the line of best fit.

Estimating values outside the range of the data using the line of best fit.

A measure of the strength and direction of a relationship between two ranked variables.

A measure of the strength and direction of a linear relationship between two variables.

Values range from -1 to +1, where -1 indicates perfect negative correlation and +1 indicates perfect positive correlation.

Values range from -1 to +1, where -1 indicates perfect negative linear correlation and +1 indicates perfect positive linear correlation.

SRCC is used for ranked data, while PMCC is used for numerical data with a linear relationship.

Data that is descriptive and non-numerical, such as colours or opinions.

Data that is numerical and can be measured, such as height or temperature.

Quantitative data that can only take specific values, such as the number of people.

Quantitative data that can take any value within a range, such as weight or time.

Data collected directly by the researcher for a specific purpose.

Data that has been collected by someone else and is used by the researcher.

Data that can be grouped into categories, such as eye colour or car brands.

Data that can be ordered or ranked, such as exam grades or survey responses.

Unbiased as every member of the population has an equal chance of being selected.

Can be time-consuming and difficult to achieve if the population is large.

Quick and easy to implement, especially with an ordered list.

Can introduce bias if the list has a hidden pattern.

Ensures all groups in the population are represented proportionally.

Time-consuming and requires detailed information about the population.

Quick and easy to carry out, and ensures representation of specific groups.

Can be biased as it relies on the researcher’s judgement to select participants.

A mean where different values are given different weights based on their importance or frequency.

Weighted mean = (Σwx) ÷ Σw, where w is the weight and x is the value.

Used when some values contribute more to the mean than others, such as in grouped data.

A circular chart divided into sectors, showing proportions of a whole.

Two or more pie charts used to compare data sets, with areas proportional to the total frequencies.

Angle = (Frequency ÷ Total frequency) × 360°.

Used to compare proportions and totals between different data sets.

Visually shows proportions and is easy to interpret.

Does not show exact values and can be hard to compare small differences.

The likelihood of an event occurring, expressed as a number between 0 and 1.

Probability = Number of favourable outcomes ÷ Total number of possible outcomes.

Events that cannot happen at the same time, e.g., rolling a 3 or a 4 on a die.

Events where the sum of their probabilities equals 1, e.g., heads and tails in a coin toss.

Events where the outcome of one does not affect the outcome of the other.

Events where the outcome of one affects the outcome of the other.

P(A or B) = P(A) + P(B) for mutually exclusive events.

P(A and B) = P(A) × P(B) for independent events.

Mean, median, and mode are used to compare the average values of data sets.

Range, interquartile range (IQR), and standard deviation are used to compare the variability of data sets.

Used to compare medians, ranges, and IQRs visually between data sets.

Used to compare distributions and find medians and quartiles of data sets.

Used to compare the frequency distribution of continuous data between data sets.

Used to compare relationships between two variables in different data sets.

Consider sample size, measures of central tendency, and spread to make fair comparisons.

A measure that shows how a value has changed compared to a base value, often expressed as a percentage.

Index number = (Value ÷ Base value) × 100.

The year or time period used as a reference point for index numbers.

Used to compare changes in data over time, such as prices or production levels.

Simplifies comparisons over time and highlights trends.

Does not show absolute values and can be affected by changes in the base year.

A table or formula showing all possible outcomes of an event and their probabilities.

A probability distribution where outcomes are distinct and countable, e.g., rolling a die.

A probability distribution where outcomes can take any value within a range, e.g., heights.

A distribution where all outcomes have equal probabilities.

A discrete probability distribution for events with two outcomes, e.g., success or failure.

The sum of all probabilities in a distribution equals 1.

A sequence of data points measured at successive time intervals.

The general direction in which data points move over time, e.g., increasing or decreasing.

Regular patterns in data that repeat over specific time periods, e.g., monthly sales.

A method to smooth out fluctuations in time series data to identify trends.

Used to identify trends, seasonal variations, and make predictions.

A line graph used to display data points over time, showing trends and patterns.

Events where the outcome of one does not affect the outcome of the other.

P(A and B) = P(A) × P(B).

Flipping a coin and rolling a die are independent because one does not affect the other.

The probability of one event occurring is the same regardless of whether the other event occurs.

The probability of an event occurring given that another event has already occurred.

P(A | B) = P(A and B) ÷ P(B), where P(A | B) is the probability of A given B.

The probability of one event depends on the occurrence of another event.

The probability of drawing a red card given that the card drawn is a heart.

A continuous probability distribution that is symmetric and bell-shaped.

A discrete probability distribution for events with two outcomes, e.g., success or failure.

Most values cluster around the mean, with fewer values at the extremes.

Defined by the number of trials (n) and the probability of success (p).

Normal is continuous and symmetric; binomial is discrete and based on trials.

Heights of people or exam scores in a large population.

Flipping a coin multiple times and counting the number of heads.

A graph showing the relationship between two variables using plotted points.

A relationship where as one variable increases, the other also increases.

A relationship where as one variable increases, the other decreases.

No apparent relationship between the two variables.

A straight line drawn on a scatter diagram to show the general trend of the data.

Estimating values within the range of the data using the line of best fit.

Estimating values outside the range of the data using the line of best fit.