Statistics and Probability

Collecting data, summarising it with an average and a range, showing it in a chart, and measuring how likely something is — plus the ways each of those can mislead.

หลักสูตรแกนกลาง / สสวท.: สถิติและความน่าจะเป็น (Statistics and Probability)ตรงกับ ม.1 บทที่ 9 สถิติ และต่อไปยังความน่าจะเป็นใน ม.3
Common Core (US): 6.SP, 7.SP
Cambridge: Lower Secondary Stage 7 — Statistics and Probability

10.1 Mode, median, mean and range

Measure	What it is	Watch out for
mode	the most common value	there may be none, or several
median	the middle value once ordered	order the data first
mean	total divided by how many	one extreme value drags it
range	largest minus smallest	a spread, not an average

The three averages and the spread

ข้อควรระวัง

The range is not an average. It measures how spread out the data is, and a question asking for "the average and the range" is asking for two different kinds of thing.

ตัวอย่าง 1

Find the mode, median, mean and range of $4, 7, 7, 9, 13$ .

วิธีทำ

1.Already in order
2.Mode: $7$ appears twice
3.Median: the third of five values, so $7$
4.Mean: $\frac{4 + 7 + 7 + 9 + 13}{5} = \frac{40}{5} = 8$
5.Range: $13 - 4 = 9$

ตอบ mode $7$ , median $7$ , mean $8$ , range $9$

ตัวอย่าง 2

Monthly salaries in thousands of baht are $15, 16, 17, 18, 200$ . Which average describes a typical worker?

วิธีทำ

1.Mean: $\frac{266}{5} = 53.2$
2.Median: $17$
3.The mean is higher than four of the five salaries, so it describes nobody

ตอบ The median, $17$ thousand baht

ทำไมถึงเป็นแบบนั้น

News reports and advertisements pick whichever average suits them. Seeing the word "average" and asking "is there an extreme value in here?" is the skill this section is really for — not the arithmetic.

📖 2 more sections of this chapter are being checked

The whole chapter is written; we read it back section by section before releasing it, because maths nobody has checked should not be on a public page. What is open is complete — nothing here is abridged.

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