Statistics - Unit 1

Information about individuals or subjects in a population

Any characteristic, numerical value, or quantity that can be measured or counted

Eye colour, height

Qualitative (categorical) and quantitative (numerical)

Discrete and continuous data

Countable data that only results in whole numbers

Ranges of values that are not exact

The collection of individuals or subjects that are being studied by the researcher

A subset of the population where the collection is made without bias and the sample is highly representative of the total population

A collection of information from every individual or subject of the population

A numerical value or quantity measuring some aspect of the population

A numerical value or quantity measuring some aspect of the population

The variation of data

Data points that are either too high or too low when compared to the other data points

A chart of the number of times each value occurs

A visual display of data in which quantities are represented by bars of equal width

Bar graphs are used for discrete data

A graph representing ranges of data

A histogram is used with continuous data

Max value - min value

Based upon the grapher’s discretion, usually a minimum of 5 bins and a maximum of 15

Range/# of classes

The ranges of values to encompass continuous data

A method of selecting a sample that will be representative of the overall population

• Every member of the population has an equal change of being selected

• The selection of any particular individual does not impact the chances of any other from being chosen

• Reduction of sample bias

• May not be representative of the population, but these derivations are due only to chance

• The population is divided into groups or members who share common characteristics such as gender, age, education level, geographic areas, etc. which are called strata

• A stratified sample has the same proportion of members from each stratum as the population does

• A simple random sample for the members of each stratum is taken

• Ensures each subgroup within the population receives proper representation'

• Many conditions have to be met, so it cannot be used for every study if you cannot classify every member of the population into a stratum

• Used to sample a fixed percent of the population

• A random starting point is chosen and every individual from that point is determined by:

  n = population size ÷ sample size

• It is simple and is therefore popular among researchers

• Low probability of contaminating data

• If every nth data point has a random characteristic the sample may disproportionately represent the population

• Made up of a conveniently available pool of respondents

• Members are chosen based on proximity rather than population representation

• Commonly used as it is prompt, simple, and economical

• Possibility of bias as some groups will be over-represented while others with be under-represented

• Since the selection is biased, there will be inaccuracies in the study

Inconsistencies in studies caused by biased selection of samples

• Survey population is divided into mutually exclusive subgroups

• Subgroups are selected with respect to known (non-random) features, traits, or interests

• Inexpensive method of selecting a sample

• Guarantees the inclusion of people you need

• Participants are not randomly drawn and may have specific characteristics meaning it is impossible to know how well they represent the groups in a population

Any factor that favours certain outcomes on responses, skewing the results, and can be unintentional or deliberate

The cumulative frequency of the previous class added to the frequency of the current class that adds to the total frequency

The frequency of a class divided by the total frequency

The measure of the location of the middle of a data with the purpose of describing a set of numerical data using a single value

Mean, median, and mode

The value(s) that occur(s) the most often, and can be more than one value depending on the distribution (ex. bimodal distributions)

The average of a set of values

xˉ = (x ₁ + x ₂ + x ₃ … + x ₙ) ÷ (n)

The mean

The middle value in a data distribution

Mean

Median

Mean or median

Mode

Mode

Mean would increase by the added value but standard deviation would not change

Mean would be multiplied by the value, standard deviation would also increase

A measure of central tendency that reflects the relative importance of data

xˉ = (∑ f * x) ÷ (n)

The mid-interval value for a class interval

When a central tendency measurement is required for a set of grouped data

An Ogive

Cumulative frequency is on the y axis and discrete data is on the x axis

Cumulative frequency is on the y axis and the upper class limit is on the x axis

To study the growth rate of data by showing the accumulation of frequency and to determine estimates of the percentiles and quartiles of the data

• S-shape used to estimate some values

• The ability to determine median by dividing the final cumulative frequency by 2

Separations of large ordered data into hundredths

Separations of large ordered data into quarters

The x point when the cumulative frequency is (n + 1) ÷ (4)

The x point when the cumulative frequency is (n + 1) ÷ (2)

The x point when the cumulative frequency is 3 * (n + 1) ÷ 4

The x point when the cumulative frequency is p * (n + 1) ÷ 100

IQR = Q ₃ - Q ₁

The distance of each data point from the mean

It shows how well a mean represents the rest of the data

When the sample sizes are small

A method of measuring spread by taking the sum of the squares of the difference between each data point and the average

σ² = (∑ (x - xˉ)²) ÷ (n)

An average of the square of the distance of each piece of data from the mean, meaning the smaller the standard deviation, the more compact the data set

σ = √((∑ (x - xˉ)²) ÷ (n))

Because when variables are grouped and the midpoint is used, the spread of observation within the interval is ignored, causing the standard deviation to be lower than the true value

A plot showing the lower extreme, lower quartile, median, upper quartile, and upper extremes of a data set, with a box showing the lower-upper quartiles and whiskers showing the extremes

Causation ≠ correlation

Pearson’s product-moment correlation

1. Start at the mean

2. Place the ruler on the mean

3. Align the ruler so that the amount of data points above and below are equal

4. Draw the line

A line of best fit

y on x, y = ax + b
x on y, x = cy + d

1. Find the mean of x

2. Find the mean of y

3. Draw two lines of best fit, one for y = ax +b and another for x = cy + d

4. Find the point at which line ax + b intersects with line cy + d

5. The calculated (x,y) coordinate is equal to (p,q)