Chapter 13

Data, Permutations and Probability (Statistics 1)

Displaying data and measuring its centre and spread, counting arrangements and selections, and the probability rules — including the conditional one that most questions are secretly about.

หลักสูตรแกนกลาง / สสวท.: สถิติและความน่าจะเป็น (Statistics and Probability)ตรงกับ ม.4 หลักการนับ และ ม.6 สถิติ (การวิเคราะห์ข้อมูลและความน่าจะเป็น)
Common Core (US): S-ID, S-CP
Cambridge: 9709 Probability & Statistics 1 — Representation of data; Permutations and combinations; Probability

13.1 Representing data, centre and spread

Mean and standard deviation, for a frequency table

\overline{x} = \frac{\sum f x}{\sum f} σ^{2} = \frac{\sum f x ^{2}}{\sum f} - \overline{x}^{2}

The second form is the one to use in an exam: it needs only the two totals, and it is what the given summary statistics are always expressed in.

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Which display for which question
- stem-and-leaf keeps every original value — use it when the actual data matter
- box-and-whisker shows median, quartiles and outliers — use it to COMPARE two sets
- histogram with unequal widths: the AREA is the frequency, not the height
- cumulative frequency is plotted against the UPPER class boundary

ตัวอย่าง

For a sample of $50$ values, $\sum x = 1250$ and $\sum x^{2} = 33, 000$ . Find the mean and the standard deviation.

วิธีทำ

1. $\overline{x} = \frac{1250}{50} = 25$
2. $σ^{2} = \frac{33 , 000}{50} - 2 5^{2} = 660 - 625$
3. $σ = 35$

ตอบ Mean $25$ , standard deviation $\approx 5.92$

ข้อควรระวัง

Comparing two data sets means comparing the CENTRE and the SPREAD, in the context of the question. "Set A has a higher mean" is half an answer; "Set A has a higher mean and a smaller spread, so those trees are taller and more uniform in height" is the whole one.

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