@?stats

What is qualatitive data?? Non-numerical values. What is categorical dtaa?? Non-numerical values. What’s an example of qualititive data?? Colour. What is quantitive data?? Numerical values. What is discrete data?? Data that can only have specific, numerical values. What’s an example of discrete data?? Shoe size Number of children What is continious data?? Data that can take any decimal value within a specified range. What is continious qualititive data?? That doesn’t exist. In $20 \leq w < 70$, what does $20$ represent?

What is a population?? The whole set of items that are of interest when collecting data. What is a sample?? A subset of a population that is intended to represent the populations. What’s an example of a population?? All humans in the UK All light bulbs in a factory All the cars in Europe What is a sampling unit?? Each individual thing in the population that can be sampled. What is a sampling frame?

What is variance?? A measure of spread that takes all values into account. What is the mathematical definition of variance, in words?? The average squared distance from the mean. What is the formula for variance?? $$ \sigma^2 = \frac{\sum (x - \bar{x}) ^ 2}{n} $$ Or $$ \sigma^2 = \frac{\sum x^2}{n} - \bar{x}^2 $$ What is the definition of the standard deviation?? The average distance from the mean. What is the formula for standard deviation?? $$ \sigma = \sqrt{\sigma^2} $$

Mean The mean is the average value. In stats, it is written as $\bar{x}$ where $x$ is the data. What does $\bar{x}$ mean?? The mean of the values in $x$. What is the notation for the mean of the values in $x$?? $\bar{x}$. What is the formula for mean?? $$ \bar{x} = \frac{\sum x}{n} $$ What does $\sum x$ mean?? The sum of the values in $x$. What is the formula for mean for frequency data?

Measures Measures are a set of summary statistics, a set of values to describe data. Measures of Location Maximum Minimum Quartiles Percentiles Deciles Measures of Centeral Tedency Mode Median Mean Measures of Spread Range Standard Deviation Interquartile range Variance When comparing data sets, what two things do you need to comment on?? A measure of location A measure of spread When comparing data sets, what measure of spread could you comment on?

Notation $x$ in Algebra vs Stats Similarities Represent the value of some quality Variables can be discrete or continuous Can be part of a larger calculation For example, $2x$ could be double the heights of everyone. This is known as [[Stats - Coding]]S . Differences Variables can represent multiple objects, like a set. Can do operations on $x$ like it’s a collection of values: $\sum x$, the sum of all values in $x$ $\bar{x}$, the mean of all values in $x$.