Describing Numerical Data

Slide 1

Describing Numerical Data

Slide 2

Two Good Papers, Two Opposite Habits

The session opens on a puzzle, not a definition. Same kind of thing, numbers measured on people, and opposite conventions. Somebody decided. On what?

Slide 3

What you will be able to do at the end of today

Slide 4

Act I · Where the Middle Is

Slide 5

Three middles, and they answer different questions

Mean, median, and mode are not three ways to say ‘average.’ They answer three different questions about the same column. The rest of the afternoon is about which question a paper is allowed to ask.

Slide 6

One value moves, and only one of them moves with it

Slide 7

Trimming the ends, and the summary that survives it

Slide 8

The spread that matches the median

Slide 9

So the gap between them describes the shape

Slide 10

A column with a floor, and why its mean would be a fiction

Years of schooling, counts, anything that cannot go below zero: the mean can sit in a place no person occupies. That is already enough to prefer a median, before anyone has drawn a histogram.

Slide 11

Reading a median off a table you did not collect

Slide 12

Act II · How Spread Out It Is

Slide 13

Means do pool, if you weight them

Slide 14

A center on its own describes almost nothing

Slide 15

Quartiles, and the middle half of the data

Slide 16

Quartiles are percentiles, and you already read those

Slide 17

The five-number summary, as a reporting standard

Slide 18

The standard deviation, in the units of the thing measured

Slide 19

Spread as a share of size

Slide 20

Where the standard deviation comes from, without the algebra

Slide 21

Two groups, two spreads, and what that tells you

Slide 22

Standard deviation is not standard error

One describes how spread out the people are. The other describes how unstable the mean would be in another sample. Mixing them is the most expensive confusion in a Table 1, and it is named here so Session 7 can own the second one properly.

Slide 23

Act III · Choosing, and the Answer to the Puzzle We Opened With

Slide 24

A change is a column too, and it has its own center and spread

Slide 25

You can audit the choice from the printed table alone

You do not need the dataset. If a paper prints a mean and an SD for a column that must be skewed, the choice is already visible. Reading becomes checking, not trusting.

Slide 26

So why did the Sylhet paper never print a mean?

The question the opening slide withheld. The answer is the shape of the columns, not a house style. Once you can see that from the printed numbers, you can say why a careful paper made the choice it made.

Slide 27

Reconstructing a mean you were never given

Slide 28

The rule, and it is shorter than the discussion

Mean and SD when the column can support them. Median and IQR when it cannot. The long discussion exists so the short rule is believed, not so it can be replaced by a slogan.

Slide 29

What to print, and in what form

Precision, units, and the digits you are entitled to. A summary that cannot be true is worse than no summary. Session 5 then owns the shape behind the choice; today only decides which pair of numbers leaves the room.

Slide 30

Precision, units, and the digits you are entitled to

Slide 31

Act IV · When One Number Will Not Do the Job

Slide 32

Summaries that cannot be true

Slide 33

When the summary is the wrong object entirely

Slide 34

The third option, and it is no longer deferred

Slide 35

Common traps, collected

Slide 36

Close

Slide 37

Before the next session