A botanist groups the heights of 40 plants into classes of width 10 cm and uses the step-deviation method with assumed mean $a = 45$ cm. She finds $\sum f u = -12$ , where $u = \frac{x - 45}{10}$ . What is the mean height?

42 cmCorrect answerYour answer44.7 cmCorrect answerYour answer48 cmCorrect answerYour answer57 cmCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Mean = $a + \frac{\sum fu}{\sum f} \times h$ .
Mean = $45 + \frac{-12}{40} \times 10 = 45 - 3 = 42$ cm.

Worth noting

44.7 cm forgets to multiply by the class width 10. 48 cm drops the minus sign, and 57 cm adds 12 to the assumed mean without dividing by 40 or multiplying by 10.

Concept: Step-deviation method for the mean
Typical timeTypical: 70 s
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A botanist groups the heights of 40 plants into classes of width 10 cm and uses the step-deviation method with assumed mean a=45a = 45a=45 cm. She finds ∑fu=−12\sum f u = -12∑fu=−12, where u=x−4510u = \frac{x - 45}{10}u=10x−45​. What is the mean height?

Explanation

A botanist groups the heights of 40 plants into classes of width 10 cm and uses the step-deviation method with assumed mean $a = 45$ cm. She finds $\sum f u = -12$ , where $u = \frac{x - 45}{10}$ . What is the mean height?