Individuals The object/units described by a set of data.
Variable Any one characteristics of an individual.
Categorical variable Variable that places an individual into one of several groups.
Nominal variable Categorical variable that is purely qualitative and unordered.
Ordinal variable Categorical variable in which data can be ranked.
Quantative variable Variable that takes numerical values for which arithmetic
operations such as adding and averaging makes sense.
Continuous variable Quantative variable that can take any real numerical value over
an interval.
Discrete variable Quantative variable that can take a limited, finite number of
values.
Outlier Individual value that falls outside the overall pattern.
Shape Unimodal, bimodal, multimodal.
Centre The value at which roughly half of the observations take smaller
values and half of the observations take larger values.
Skewed right Positively skewed, the right side of the histogram extends much
farther out than the left side (peak at the left).
Skewed left Negatively skewed, the left side of the histogram extends much
farther out than the right side (peak at the right).
Time plot A figure that plots each observation against the time at which it
was measured. Time is put on the horizontal scale and the variable
that is measured on the vertical scale.
Median M The midpoint of a distribution, the number such that half the
observations are smaller and the other half are larger, resistant
𝑛+1
measure of centre. Location of the median is 𝑀 = .
2
Mean Ordinary arithmetic average, non-resistant measure of centre. 𝑥̅ =
𝑥1+𝑥2+𝑥𝑛 1
. In a more compact notation 𝑥̅ = 𝑛 ∑ 𝑥𝑖.
𝑛
Resistant measure The value is not influenced by outliers.
First quartile Median of the observations whose position in the ordered list is
to the left of the overall median.
, Third quartile Median of the observations whose position in the ordered list is
to the right of the overall median.
IRQ The interquartile range is the distance between the first and third
quartiles 𝐼𝑄𝑅 = 𝑄3 − 𝑄1.
Standard deviation A non-resistant measure of spread. The standard deviation and its
squared value (variance s2) measure spread by looking at how far
the observations are from their mean. The simple standard
deviations s is the square root of the sample variance s2.
(𝑥1−𝑥̅ )2 +(𝑥2−𝑥̅ )2 +(𝑥𝑛−𝑥̅ )2 1
𝑠2 = or 𝑠 2 = 𝑛−1 ∑(𝑥𝑖 − 𝑥̅ )2 .
𝑛−1
Suspicion An observation is a suspected outlier if it falls more than
1.5 × 𝐼𝑄𝑅 above the third quartile of below the first quartile.
Scatterplot A scatterplot shows the relationship between two quantative
variables measured on the same individuals. The values of one
variable appear on the horizontal axis, and the values of the other
variable appear on the vertical axis. The explanatory variable is
always plotted on the x-axis and the response variable is always
plotted on the y-axis.
Direction Left, right, up, down. Measured by correlation (linear).
Form Linear, hyperbolic, etc.
Strength Strength is measured by correlation (linear relationship).
Positive association Above-average values of one variable tend to accompany above-
average values of the other, and below-average values also tend
to occur together.
Negative association Above-average values of one variable tend to accompany below-
average values of the other, and vice versa.
Correlation Measures the direction and strength of a linear relationship
between two quantative variables.
1 𝑥𝑖−𝑥̅ 𝑦𝑖−𝑦̅
Correlation 𝑟 = 𝑛−1 ∑( )( ).
𝑠𝑥 𝑠𝑦
LSRL The least-squares regression line of y on x is the line that makes
the sum of the squared vertical distances of the data points from
Variable Any one characteristics of an individual.
Categorical variable Variable that places an individual into one of several groups.
Nominal variable Categorical variable that is purely qualitative and unordered.
Ordinal variable Categorical variable in which data can be ranked.
Quantative variable Variable that takes numerical values for which arithmetic
operations such as adding and averaging makes sense.
Continuous variable Quantative variable that can take any real numerical value over
an interval.
Discrete variable Quantative variable that can take a limited, finite number of
values.
Outlier Individual value that falls outside the overall pattern.
Shape Unimodal, bimodal, multimodal.
Centre The value at which roughly half of the observations take smaller
values and half of the observations take larger values.
Skewed right Positively skewed, the right side of the histogram extends much
farther out than the left side (peak at the left).
Skewed left Negatively skewed, the left side of the histogram extends much
farther out than the right side (peak at the right).
Time plot A figure that plots each observation against the time at which it
was measured. Time is put on the horizontal scale and the variable
that is measured on the vertical scale.
Median M The midpoint of a distribution, the number such that half the
observations are smaller and the other half are larger, resistant
𝑛+1
measure of centre. Location of the median is 𝑀 = .
2
Mean Ordinary arithmetic average, non-resistant measure of centre. 𝑥̅ =
𝑥1+𝑥2+𝑥𝑛 1
. In a more compact notation 𝑥̅ = 𝑛 ∑ 𝑥𝑖.
𝑛
Resistant measure The value is not influenced by outliers.
First quartile Median of the observations whose position in the ordered list is
to the left of the overall median.
, Third quartile Median of the observations whose position in the ordered list is
to the right of the overall median.
IRQ The interquartile range is the distance between the first and third
quartiles 𝐼𝑄𝑅 = 𝑄3 − 𝑄1.
Standard deviation A non-resistant measure of spread. The standard deviation and its
squared value (variance s2) measure spread by looking at how far
the observations are from their mean. The simple standard
deviations s is the square root of the sample variance s2.
(𝑥1−𝑥̅ )2 +(𝑥2−𝑥̅ )2 +(𝑥𝑛−𝑥̅ )2 1
𝑠2 = or 𝑠 2 = 𝑛−1 ∑(𝑥𝑖 − 𝑥̅ )2 .
𝑛−1
Suspicion An observation is a suspected outlier if it falls more than
1.5 × 𝐼𝑄𝑅 above the third quartile of below the first quartile.
Scatterplot A scatterplot shows the relationship between two quantative
variables measured on the same individuals. The values of one
variable appear on the horizontal axis, and the values of the other
variable appear on the vertical axis. The explanatory variable is
always plotted on the x-axis and the response variable is always
plotted on the y-axis.
Direction Left, right, up, down. Measured by correlation (linear).
Form Linear, hyperbolic, etc.
Strength Strength is measured by correlation (linear relationship).
Positive association Above-average values of one variable tend to accompany above-
average values of the other, and below-average values also tend
to occur together.
Negative association Above-average values of one variable tend to accompany below-
average values of the other, and vice versa.
Correlation Measures the direction and strength of a linear relationship
between two quantative variables.
1 𝑥𝑖−𝑥̅ 𝑦𝑖−𝑦̅
Correlation 𝑟 = 𝑛−1 ∑( )( ).
𝑠𝑥 𝑠𝑦
LSRL The least-squares regression line of y on x is the line that makes
the sum of the squared vertical distances of the data points from
