Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits: Lower limit: Q1 − 1.5 ✕ (IQR) Upper limit: Q3 + 1.5 ✕ (IQR) where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows: 65 72 68 64 60 55 73 71 52 63 61 74 69 67 74 50 4 75 67 62 66 80 64 65 (a) Find the value of the interquartile range (IQR). (b) Multiply the IQR by 1.5 and find the lower and upper limits. (Enter your answers to one decimal place.)
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.
Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits:
Lower limit: Q1 − 1.5 ✕ (IQR)
Upper limit: Q3 + 1.5 ✕ (IQR)
where IQR is the
65 72 68 64 60 55 73 71 52 63 61 74
69 67 74 50 4 75 67 62 66 80 64 65
(a) Find the value of the interquartile range (IQR).
(b) Multiply the IQR by 1.5 and find the lower and upper limits. (Enter your answers to one decimal place.)
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