CH1 Descriptive Statistics
Population = all items under consideration for particular study.
o a parameter is a numerical value calculated on the pop.
Sample = a portion of a population (use)
o a statistic is a numerical value calculated on the samp.
Data Types
There are 2 main data types:
o Numerical (quantitative) data = counted or measured response values.
- Discrete data (counting - can be observed exactly)
- Continuous data (measuring - can only be observed approximately)
o Categorical (qualitative) data = finite number of categories represent the
response values in the data.
Measurement scales
Numerical (quantitative) data:
o Interval scale = difference between numerical measurements are
meaningful, but does not have a true zero.
o Ratio scale = difference between measurements are meaningful and
comprise of a true zero.
- Zero → empty / nothing
2 Categorical (qualitative) data.
o Nominal scale = the categories of the data cannot be ordered in a logical
way.
o Ordinal scale = the categories of the data can be ordered in a natural
way.
- occurs when numerical data are converted to categories.
, Summary Statistics
Measures of central tendency
o Mean
o Median
o Mode
Relationship between them:
- mean > median > mode → positively skewed / to the right
- mean < median < mode → negatively skewed / to the left
- mean = median = mode → symmetric
o Quantiles consider a specific location in the sorted data set.
- k = p( n + 1 )
- use percentile.exc(array, Q)
- Q1 = 25%, Q2 = 50% = median, Q3 = 75%
Measures of variation/spread
o Range = distance btwn max and min observed value.
- R = xn – x1
- IQR indicates distance over which middle 50% of data is spread
IQR = Q1 – Q3
o Variance & standard deviation = measure of how far sample values are
away from the mean.
Population = all items under consideration for particular study.
o a parameter is a numerical value calculated on the pop.
Sample = a portion of a population (use)
o a statistic is a numerical value calculated on the samp.
Data Types
There are 2 main data types:
o Numerical (quantitative) data = counted or measured response values.
- Discrete data (counting - can be observed exactly)
- Continuous data (measuring - can only be observed approximately)
o Categorical (qualitative) data = finite number of categories represent the
response values in the data.
Measurement scales
Numerical (quantitative) data:
o Interval scale = difference between numerical measurements are
meaningful, but does not have a true zero.
o Ratio scale = difference between measurements are meaningful and
comprise of a true zero.
- Zero → empty / nothing
2 Categorical (qualitative) data.
o Nominal scale = the categories of the data cannot be ordered in a logical
way.
o Ordinal scale = the categories of the data can be ordered in a natural
way.
- occurs when numerical data are converted to categories.
, Summary Statistics
Measures of central tendency
o Mean
o Median
o Mode
Relationship between them:
- mean > median > mode → positively skewed / to the right
- mean < median < mode → negatively skewed / to the left
- mean = median = mode → symmetric
o Quantiles consider a specific location in the sorted data set.
- k = p( n + 1 )
- use percentile.exc(array, Q)
- Q1 = 25%, Q2 = 50% = median, Q3 = 75%
Measures of variation/spread
o Range = distance btwn max and min observed value.
- R = xn – x1
- IQR indicates distance over which middle 50% of data is spread
IQR = Q1 – Q3
o Variance & standard deviation = measure of how far sample values are
away from the mean.
