Unit 1, Exploring one variable data

Variables

Categorical

Quantitative

Assigns labels that place each individual into a particular group, known as category

Takes number values that are quantities; counts or measurements.

Could be represented as Bar graph or two way table

Could represented with dotplots, stemplots and histograms

Symmetric, left skewed or right skewed

Describing a distribution

Outlieres

Center

Shape

Variability

Symmetric, unimodal, bimodal, skewed

Identify whether there is a gap between the intervals, if there is, potential outlier is observed

1.5IQR rule, Q1-1.5(IQR)< X < Q3+1.5(IQR)

Mean(Symmetric), Median(Skewed graph)

Standard deviation( Symmetric), IQR(Skewed)

Making and Interpreting Boxplots

Displays quantitative data through five number summary.


  1. Minimum
  2. Maximum
  3. First quartile(Q1)
  4. Median(Q2)
  5. Third quartile(Q3)

image

When comparing two distribution, comparing words must be included.


Comparison words examples:
larger, higher, compared to, same, different, smaller, less than, etc.

Normal Distribution

Described by a symmetric, single peaked, bell shaped density curve called a normal curve

Standard Normal Distribution
Mean=0
Standard Deviation=1

Empirical Rule: 68-95-99.7

Z-Score

image

The number of standard deviations a value is from the mean

image

Standardized Score:
indicates how many standard deviations a datum is above or below the population/sample mean

image

image

image

Steps of making a boxplot
Find the five number summary
Identify outliers
Draw and label the axis
Draw a box Mark the median.
Draw whiskers

Be sure a Key is included. Ex: 10 | 4= 10.4

Unbiased Biased Estimator: Sample mean/proportion=population mean/proportion