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Answer and Step-by-step explanation:
(a) To calculate the sample <u>mean</u>:
x = ∑xi / n
x = 12.5375
Sample <u>median</u> is the middle term of the set. To determine it, put the data in order: 8.1,9.3,11,12.5,12.6,14.2,14.9,17.7
There are 8 numbers in the set, so the middle term is the average of 12.5 and 12.6:
median =
median = 12.55
The 12.5% trimmed mean is the mean calculated excluding the 12.5% largest and the 12.5% smallest values form the sample and taking the average of the remaining numbers.
In this case, there are 8 numbers:
12.5% of 8 = 1
So, to find the trimmed mean:
= 12.42
The results show that the three measures of center are similar, indicating little skewness to the data set, i.e., the graph is a bell shaped one.
(b) The smallest sample could be increased by any number lower than 12.5, since the last number affects directly the sample median.
(c) No, the values obtained in (a) can be used directly: The mean in psi can be rewritten in ksi:
(12.5375) psi . = 5.7 ksi