Statistics

Averages from grouped data, the charts this syllabus is particular about — histograms with unequal widths and cumulative frequency — and what a scatter graph can and cannot prove.

หลักสูตรแกนกลาง / สสวท.: สถิติและความน่าจะเป็น (Statistics and Probability)ครอบคลุม ม.2 บทที่ 7 · ม.3 บทที่ 10 · ม.6 สถิติและการวิเคราะห์ข้อมูล
Common Core (US): S-ID, 8.SP
Cambridge: IGCSE 0580 — Topic 9: Statistics (Core and Extended)

12.1 Averages from grouped data

Estimating the mean

1Find the midpoint of each class
2Multiply each midpoint by its frequency
3Add the products, and add the frequencies
4Divide — and call it an ESTIMATE

ข้อควรระวัง

Grouped data gives an estimated mean, a MODAL CLASS and a class containing the median — never exact values. Naming a single number for the mode claims information the table does not contain.

ตัวอย่าง

Estimate the mean of: $0 < x \leq 10$ (freq $6$ ), $10 < x \leq 20$ (freq $14$ ), $20 < x \leq 30$ (freq $10$ ).

วิธีทำ

1.Midpoints: $5$ , $15$ , $25$
2.Products: $30$ , $210$ , $250$ — total $490$
3.Total frequency: $30$
4. $490 \div 30$

ตอบ An estimated mean of $16.3$ (3 s.f.)

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