Question

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 limitsLower 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 7469 67 74 50 4 75 67 62 66 80 64 65(a) Make a box-and-whisker plot of the data.
(b) Find the value of the interquartile range (IQR).(c) Multiply the IQR by 1.5 and find the lower and upper limits. (Enter your answers to one decimal place.)lower limit upper limit

Answer 1

Answer:

a) The box plot is attached.  b) The lower limit is 46.5 and the upper limit is 86.5.

Step-by-step explanation:

The first step in creating a box plot is to order the data from least to greatest:

4,50,52,55,60,61,62,63,64,64,65,65,66,67,67,68,69,71,72,73,74,74,75,80

The median is the middle data value.  This is between 65 and 66; this makes it

(65+66)/2 = 131/2 = 65.5.

The lower quartile, Q1, is the middle of the lower half of data.  This is between 61 and 62; this makes it

(61+62)/2 = 123/2 = 61.5.

The upper quartile, Q3, is the middle of the upper half of data.  This is between 71 and 72; this makes it

(71+72)/2 = 143/2 = 71.5.

This makes the interquartile range, IQR, 71.5-61.5 = 10.

The lower limit for outliers will be

61.5-1.5(10) = 61.5-15 = 46.5.

The upper limit for outliers will be

71.5+1.5(10) = 71.5+15 = 86.5.