What is a variable?
A variable is any characteristic of the population being studied or observed.
For example, if a statistician surveys 953 Canadian males who play recreational sports, asking their age, what sport they play, and how often they play, the example includes 3 variables.
What is the population?
The population is the entire group you want to know about in a study.
For example, if a researcher wants to know the attitudes of North American women on violence against women, and surveys 450 college and university students, the population of the study is North American women.
Types of Sampling
Every selection is likely to be selected and every combination of selections is likely to be selected
Has a starting point, and then every nth number is selected
The data is divided into groups, and a sample from each group is selected
Data is divided into groups, and a random sample of the groups is selected. All members of the selected groups are surveyed.
Data is divided into groups, a random sample of groups is chosen, and a random sample of members from the chosen groups are selected
Used simply because it is easily accessible
Obtained by making a general appeal for responses
Correlation indicates the strength and direction of a linear relationship between two variables.
Correlation analysis involves generating a single number from the data, which is called the correlation coefficient and is represented by r.
The value of r is always between -1 and 1.
A coefficient of 0 indicates no linear correlation.
A coefficient between 0 and 1 indicates a positive correlation. A number closer to 1 indicates a stronger positive correlation, and a number closer to 0 indicates a weaker positive correlation.
A number between -1 and 0 indicates a negative correlation. A number closer to -1 indicates a stronger negative correlation, and a number closer to 0 indicates a weaker negative correlation.
For example, if r^2 = 0.9875878, a strong positive correlation is present between two variables.
If data is bunched towards the right, it is a positive skew.
If data is bunched towards the left, it is a negative skew.
If data is distributed evenly, there is no skew.
Calculating the Mean
To calculate the mean of a group of data, add up all the values, then divide by the number of values.
The median is the middle number when data is arranged in ascending order.
If there is an even number of data, there will be two middle numbers. If there are two middle numbers, the median is the mean of the two numbers.
If there are n data points and n is odd, the middle data point is n + 1 / 2
If n is even, the middle two numbers are the n / 2 and n / 2 + 1 numbers
Measure of Spread
The measure of spread is the degree to which data differ from, or are spread out from, the centre.
Range is the difference between minimum and maximum values.
It shows the overall spread of data.
Quartiles are a measure of spread.
A quartile is any of the three values that divide the sorted data set into four equal parts, so that each part represents one-fourth of the data set.
To find quartiles, first use the median to split the data in half.
Q1 is found by finding the median of the half of data below the median of the entire set of data.
Q2 is the median of the entire set of data.
Q3 is found by finding the median of the half of data above the median of the entire data.
Percentile is the value of a variable below which a certain percentage of observations fall.
Percentile is used to rank an individual's position within a set of data.
For example, the 20th percentile is the value below which 20% of the observations are found
Variance & Standard Deviation
Variance and standard deviation are measures of spread.
Deviation is the distance between a particular value and the mean.
Variance is determined by calculating the average of the squares of all deviations for a particular set of data