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# Measures of Central Tendency: Mean, Median; constructing CI

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The breaking strengths of cables produced by a certain manufacturer have a standard deviation of pounds. A random sample of newly manufactured cables has a mean breaking strength of pounds. Based on this sample, find a confidence interval for the true mean breaking strength of all cables produced by this manufacturer. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

51,56,61,61,65,69,72,73,73,73,74,75,76,79,79,81,83,87,87,93,95

Which measures of central tendency do not exist for this data set?
Mean
Median
None
None of these measures

Suppose that the measurement 95 (the largest measurement in the data set) were replaced by 148. Which measures of central tendency would be affected by the changed? Choose all that apply.
Mean
Median
None
None of these measures

Suppose that starting with the original data set the largest measurement were to removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.

Mean
Median
None
None of these measures

Which of the following best describes the distribution of the orginal data set

Negative skewed
Positively skewed
Roughly skewed symmetrical

#### Solution Preview

2.
(a) 90%CI = (1729.4,1770.6).

(b) Mean=74.4 [add the 21 numbers and then divide by 21]
Median=74 [middle number in the ordered list]

(c) Mean=76.95
The mean will be affected by the change. The median will ...

#### Solution Summary

In this problem we examine the mean and the median. How is the mean and median affected by removing a value from a set of data? How is the mean and median affected by changing a value in a data set. These questions are looked into after the mean and median of a set of data is calculated. Step-by-step solution is provided. 95% confidence interval about the mean is calculated, as well. A Word document is included.

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