Cordless phones In their October 2003 issue, Consumer Reports evaluated the price and performance of 23 models of cordless phones. Computer output gives these summaries for the prices: Min Q1 Median Q3 Max Mean SD 15 30 50 110 200 71.75 52.08 a. Were any of the prices outliers? Explain how you made your decision. b. One of the manufacturers advertises a cordless phone "economy-priced at only $31.95." Would you consider that to be a very low price? Explain.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Cordless phones In their October 2003 issue, Consumer Reports evaluated the price and performance of 23
models of cordless phones. Computer output gives these summaries for the prices:
Min Q1 Median Q3 Max Mean SD
15 30 50 110 200 71.75 52.08
a. Were any of the prices outliers? Explain how you made your decision.
b. One of the manufacturers advertises a cordless phone "economy-priced at only $31.95." Would you
consider that to be a very low price? Explain.
Given:
Summary output
| Min | Q1 | Median | Q3 | Max | Mean | SD |
| 15 | 30 | 50 | 110 | 200 | 71.75 | 52.08 |
(a) Were any of the prices outliers? Explain how you made your decision.
Data values not following expected patterns are called Outliers.
Outliers can be identified using Interquartile range.
Interquartile range is calculated using the formula:
Any data value less than the lower limit (-90) or greater than the upper limit (230) is treated as an outlier.
Since, the min value is 15 which is greater than the lower limit, there is no lower outlier.
Max value is 200 which is less than the upper limit.
Thus, there are no outliers.
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