← Data Science learning path0%
02
Week 2 · 60 slides + Lab 2
Describing Data
Measures of central tendency, dispersion, distribution shape and standardisation.
Not started yet
Start Quiz mastery0%
What you’ll take away
- Number + unit + people counted + limitation.
- Mean balances; median finds the middle; mode finds the most common.
- Square, add, divide, square root.
- Show the path, not only the answer.
- Sort first. State the rule.
- Fence is a rule; whisker is a recorded value.
- The picture can reveal what the summary hides.
- The percentages need the normal-model assumption.
- Z is distance, not rank.
- Use your case; explain your choice.
Lecture topics
The summary contract; Mean, median and mode; Variance and standard deviation; Worked eight-number calculation; Quartiles, percentiles and conventions; Range, fences and boxplots; Shape, histograms and hidden groups; The normal-model rule; Z-scores: relative to which group?; Lab 2 completion map
Lessons
- The summary contractAn average is only useful if the reader knows what was averaged and how many measurements were available.6 min
- Mean, median and modeThese are three ways to describe the centre of data. They answer different questions and react differently to unusual values.7 min
- Variance and standard deviationStandard deviation, or SD, describes how much values spread around the mean. Variance is the step before taking the square root.7 min
- Worked eight-number calculationWriting the steps makes your answer easier to check and helps you avoid mixing sample and population formulas.6 min
- Quartiles, percentiles and conventionsQuartiles split the ordered data into sections. Different agreed rules can give different quartiles in a small dataset.6 min
- Range, fences and boxplotsA boxplot gives a compact picture of the middle, spread and unusual values. A review flag is a reason to check a record, not a command to delete it.7 min
- Shape, histograms and hidden groupsData can have tails, gaps or several groups. Two datasets can share the same mean and SD but need different decisions.7 min
- The normal-model ruleFor a roughly normal, bell-shaped distribution, about 68%, 95% and 99.7% lie within one, two and three SD of the mean.6 min
- Z-scores: relative to which group?A z-score tells you how many reference SDs a value lies above or below the reference mean. It has no units.7 min
- Lab 2 completion mapThe lab asks you to calculate, interpret and defend choices using your own generated case. Understanding the result matters more than copying output.7 min
Practise this week · Lab 2: What an average hides8 guided sections · Use your own case to calculate, plot and explain the data.
Key terms
- Valid n
- The number of observed values used.
- Missing count
- The eligible measurements not available.
- Mean
- Total divided by observed count.
- Median
- Middle after sorting.
- Mode
- Most frequent value.
- Deviation
- Value minus mean.
- Variance
- Average squared deviation under the chosen divisor.
- SD
- Square root of variance.
- Working
- The intermediate calculations that justify your result.
- Rounding
- Shortening a number for display.
- Q1
- 25th percentile.
- Q2
- Median.
- Q3
- 75th percentile.
- IQR
- Q3−Q1.
- Fence
- Calculated review limit.
- Whisker
- Most extreme observed value still inside a fence.
- Range
- Maximum−minimum.
- Skew
- A longer tail in one direction.
- Bimodal
- Two main peaks.
- Bin
- An interval used by a histogram.
- Normal model
- A particular bell-shaped distribution.
- Approximation
- A useful estimate, not an exact promise.
- Reference group
- The group that supplies the mean and SD.
- Percentile
- Position in an ordered distribution.
- Case code
- Identifies your generated version.
- Interpretation
- Explaining what a number means for the question.
Practice this topic60 questions · earn XP and build your streak