📊 Statistics

What is Statistics?
Statistics is the science of collecting, organizing, and interpreting data.
Statistical Question: A question that expects variability in the answers. Different people would give different answers.
Non-Statistical Question: A question that expects a single answer. Everyone would give the same answer.
Statistical QuestionNon-Statistical QuestionHow tall are students in our class?How tall is the teacher?What is the favorite color of 6th graders?What is your favorite color?How many minutes do people spend on homework?How many minutes are in an hour?What are the ages of students in the school?How old is the principal?

Four Measures of Central Tendency:
MeasureDefinitionHow to FindExample: 2,4,6,8,10MeanAverageSum ÷ Count(2+4+6+8+10)/5 = 6MedianMiddle valueOrder, find middle2,4,6,8,10 → 6ModeMost frequentFind most commonNo mode (all appear once)RangeSpreadMax - Min10 - 2 = 8When to Use Each:
MeasureBest Used WhenMeanData is symmetrical, no outliersMedianData has outliers (very high/low values)ModeData has repeating values (favorite colors)RangeWant to know spread of data

What is a Box Plot (Box-and-Whisker Plot)?
A box plot shows how data is spread out using 5 key numbers:
Minimum Q1 Median Q3 Maximum
│ │ │ │ │
├────────┼───────┼───────┼────────┤
│ │ │ │ │
└─Whisker┴─Box───┴───────┴─Whisker─┘The 5-Number Summary:
TermMeaningExample (data: 1,3,5,7,9,11,13)MinimumSmallest value1Q1Lower quartile (25th percentile)3MedianMiddle value (50th percentile)7Q3Upper quartile (75th percentile)11MaximumLargest value13What is a Histogram?
A histogram is a bar graph that shows frequency (how many) of data in intervals (bins).
Histogram of Test Scores:

Frequency
10│ ┌─┐
9│ │ │
8│ │ │
7│ ┌─┐│ │
6│ │ ││ │
5│ │ ││ │ ┌─┐
4│ ┌─┐│ ││ │ │ │
3│ │ ││ ││ │ │ │
2│ │ ││ ││ │ │ │
1│ │ ││ ││ │ │ │
0└──┴─┴┴─┴┴─┴──┴─┴──
50-59 60-69 70-79 80-89 90-100
Score Range