High School

Consider the following observations on shear strength of a joint bonded in a particular manner:
30.0, 4.4, 33.1, 66.7, 81.5, 22.2, 40.4, 16.4, 73.7, 36.6, 109.9

Determine the value of the sample mean. Report answers correct to two decimal places.

Answer :

To find the sample mean of the given observations on shear strength, we'll follow these steps:

  1. Add all the observations together: We have the following values:
    [tex]30.0, 4.4, 33.1, 66.7, 81.5, 22.2, 40.4, 16.4, 73.7, 36.6, 109.9[/tex]
    Sum them up:
    [tex]30.0 + 4.4 + 33.1 + 66.7 + 81.5 + 22.2 + 40.4 + 16.4 + 73.7 + 36.6 + 109.9 = 515.9[/tex]

  2. Count the number of observations: There are a total of 11 observations.

  3. Calculate the mean: Divide the sum of the observations by the number of observations:
    [tex]\text{Mean} = \frac{515.9}{11} \approx 46.90[/tex]

Therefore, the sample mean of the given observations is approximately [tex]46.90[/tex] when rounded to two decimal places.

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