A student makes 9 measurements of the wavelength of a 40 kHz sound wave and find

Question

A student makes 9 measurements of the wavelength of a 40 kHz sound wave and finds the following values:

Wave length (cm) : 0.91 0.87 0.86 0.85 0.85 0.88 0.86 0.86 0.85.

The student is considering rejecting the first measurement as a bad data point.

(a) What is the mean of the last 8 measurements? (b) What is the standard deviation of the last 8 measurements?

(c) What is the discrepancy between the first measurement and the mean of the last 8 measurements?

(d) Should the student reject the first measurement? Why or why not?

Explanation / Answer

a)

Mean =Sum of all the X values /No of values of X =(0.87+ 0.86+ 0.85+ 0.85+ 0.88+ 0.86+ 0.86+ 0.85)/8=6.88/8 =0.86

b)

Standard deviation(sigma) =Sqrt(Sigms(X-M)2/(n-1) =0.01069

c)

The discrepancy between the first measurement and the mean of the last 8 measurements =0.91-0.86 =0.05

d)

Also the 0.91 is in 5sigma away from the mean

so, it is better to reject it

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