Statistics and Probability

Averages from grouped data, scatter graphs and what correlation does not prove, and the probability of two events happening together.

หลักสูตรแกนกลาง / สสวท.: สถิติและความน่าจะเป็น (Statistics and Probability)ตรงกับ ม.3 บทที่ 9 ความน่าจะเป็น และบทที่ 10 สถิติ
Common Core (US): S-ID, S-CP, 8.SP
Cambridge: Lower Secondary Stage 9 — Statistics and Probability

11.1 Averages from grouped data

Once data is grouped into class intervals the individual values are gone. Everything from here is an estimate, and saying so is part of the answer.

Estimating the mean

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

ตัวอย่าง

Estimate the mean from: $0$ – $10$ (frequency $4$ ), $10$ – $20$ ( $7$ ), $20$ – $30$ ( $9$ ).

วิธีทำ

1.Midpoints: $5$ , $15$ , $25$
2.Products: $20$ , $105$ , $225$ — total $350$
3.Total frequency: $20$
4. $350 \div 20$

ตอบ An estimated mean of $17.5$

ข้อควรระวัง

You cannot find an exact mode or median from grouped data either — only the MODAL CLASS and the class containing the median. Naming a single value implies information the table does not hold.

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