Describing Numerical Data

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Subject: Statistics I

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Unit 3: Describing Numerical Data

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Week 3 syllabus map

1. L3.1: Describing Numerical Data - Frequency Tables for Numerical Data
2. AQ3.1: Activity Question 1
3. L3.2: Describing Numerical Data - Mean
4. AQ3.2: Activity Question 2
5. L3.3: Describing Numerical Data - Median and Mode
6. AQ3.3: Activity Question 3
7. L3.4: Describing Numerical Data - Measures of Dispersion - Range, Variance and Standard Deviation
8. AQ3.4: Activity Question 4
9. L3.5: Describing Numerical Data - Percentiles, Quartiles, and Interquartile Range

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How to use this week

• Learn the table or definition first, then solve one numeric example by hand.
• Keep one formula sheet for:
  • mean
  • median
  • mode
  • range
  • variance
  • standard deviation
  • quartiles
  • interquartile range
• For any summary measure question, first ask:
  1. is the data raw or grouped?
  2. is the variable numerical?
  3. do I need center or spread?
  4. is there an outlier issue?

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Week 3 exam traps

• Mean is sensitive to extreme values.
• Median requires ordered data.
• Mode may be absent or may be more than one value.
• Range depends only on smallest and largest values.
• Standard deviation is not the same as variance.
• Quartiles split ordered data into parts; they are not random cut points.
• Interquartile range uses Q3 - Q1, not Q3 / Q1.

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Final revision checklist

• build a simple numerical frequency table
• compute mean from raw values
• find median and mode correctly
• explain range, variance, and standard deviation
• identify percentiles and quartiles from ordered data
• use IQR to describe middle spread