6.I.1 — Identify statistical questions.
Step 01 of 04
A statistical question anticipates VARIABILITY in the answer — different observations would give different values.
Step 02 of 04
Examples — statistical.
| "How tall is each student in my class?" | →different heights expected |
| "What is the daily high temperature this week?" | →varies day to day |
| "How many siblings do students have?" | →varies per student |
Step 03 of 04
Examples — NOT statistical.
| "How tall am I?" | →one specific value, no variability |
| "What is the temperature right NOW outside?" | →one value at one moment |
| "How many days in February?" | →fixed answer |
Step 04 of 04
The point: statistics is the science of describing, comparing, and reasoning about VARIABILITY in data. If there's no variability, no statistics needed.
Key insight
Statistical question = expects variation in answers. "How tall am I?" is one number; "How tall are people in my class?" is many numbers — that's statistical.
6.I.2 — Mean, median, mode, range.
Step 01 of 04
Four basic summary statistics.
| Mean (average) | →sum / count |
| Median | →middle value when sorted |
| Mode | →most frequent value (could be more than one, or none) |
| Range | →max − min |
Step 02 of 04
Worked example. Data: 4, 7, 7, 9, 13.
| Mean | →(4+7+7+9+13)/5 = 40/5 = 8 |
| Median | →7 (middle of sorted list) |
| Mode | →7 (appears twice) |
| Range | →13 − 4 = 9 |
Step 03 of 04
Even count → median is average of two middle values.
Data: 3, 5, 8, 12. Middle two are 5 and 8. Median = (5 + 8)/2 = 6.5.
Step 04 of 04
When to use which?
| Mean | →good for symmetric data without outliers |
| Median | →better when there are outliers (resistant) |
| Mode | →best for categorical data or to find most popular |
Key insight
Mean averages everything — affected by outliers. Median is the middle — outlier-resistant. Mode counts frequency. Range measures spread (min to max).
6.I.3 — Dot plots and histograms.
Step 01 of 04
Dot plot = same as line plot. Each dot represents one data point above its value on a number line.
Histogram = bars showing frequency in BINS (intervals), not individual values. Useful for larger datasets.
Step 02 of 04
When to use which.
| Small dataset (n < 30) | →dot plot — see every point |
| Larger dataset | →histogram — group into bins |
| Few unique values | →dot plot |
| Many unique values | →histogram |
Step 03 of 04
Reading a histogram. The bar heights show the COUNT (or frequency) in each bin. The width of each bin is the range of values it covers.
Step 04 of 04
Example. Test scores grouped: 60–69 (4 students), 70–79 (10), 80–89 (12), 90–99 (5). Total = 31 students. Most common range: 80–89.
Key insight
Dot plots show every data point; histograms group data into bins. Both reveal shape (center, spread, skew) of the distribution.
6.I.4 — MAD and IQR (intro).
Step 01 of 04
Two ways to measure SPREAD.
| MAD | →mean absolute deviation — average distance from the mean |
| IQR | →interquartile range — Q3 − Q1, the spread of the middle 50% |
Step 02 of 04
Compute MAD. Find the mean. Find each value's distance from the mean (absolute value). Average those distances.
Data: 4, 7, 7, 9, 13. Mean = 8. Distances: 4, 1, 1, 1, 5. MAD = (4+1+1+1+5)/5 = 12/5 = 2.4.
Step 03 of 04
Compute IQR. Sort, find Q1 (median of LOWER half) and Q3 (median of UPPER half). IQR = Q3 − Q1.
Data: 3, 5, 7, 8, 11, 14, 15. Median = 8. Lower half: 3, 5, 7 → Q1 = 5. Upper half: 11, 14, 15 → Q3 = 14. IQR = 14 − 5 = 9.
Step 04 of 04
Larger MAD or IQR = data is more SPREAD OUT. Smaller = data is tightly clustered.
Key insight
MAD: average distance from the mean. IQR: range of the middle 50%. Both measure SPREAD. MAD goes with mean; IQR goes with median.