Answer:
54.80 MPa to 55.92 MPa
Step-by-step explanation:
Sample mean fracture strength (x) = 55.36 MPa
Sample standard deviation (s) = 3.99 MPa
Sample size (n) = 196.
The upper and lower bounds for a 95% confidence interval are given by:
The upper and lower bounds of the confidence interval are;
The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa
1) Mean of the set of data: 29.88
2) Mean absolute deviation: 10.13
3) See explanation
Step-by-step explanation:
1)
The mean of a set of data it is calculated as
where
N is the number of data in the set
is the value of each point in the dataset
For the set of data in this problem, we have:
And the number of values is
N = 8
Therefore, we can calculate the mean:
2)
The mean absolute deviation of a set of data is given by
where
N is the number of values in the dataset
are the single values
is the mean of the dataset
The dataset here is
The mean, calculated in part 1), is
And
N = 8
Therefore the mean absolute deviation is
3)
The mean of a dataset is the sum of the single values of the dataset divided by the number of values. The mean represents the value for which, if the dataset would have N values all equal to
, the sum of the values of the dataset would be the same as the sum of the actual values.
The mean absolute deviation for a set of data represents the average of the absolute deviations of the single points from the mean of the dataset. This quantity gives a measure of the "dispersion" of the points around the mean: in fact, the larger the mean absolute deviation is, the more the points are "spread" around the mean of the dataset. Instead, if the mean absolute deviation is small, it means that the points are closer to the mean value.
Learn more about mean and spread of a distribution:
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