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

Required:
Make a box-and-whisker plot of the data.

Kindly check attached picture

Step-by-step explanation:

Given the data:

65 72 68 64 60 55 73 71 52 63 61 74

69 67 74 50 4 75 67 62 66 80 64 65

The box and whisker plot generated from the data above can be found in the picture below : The asterisked point on the plot is the value of the Outlier.

Using calculator :

Q1 = 61.25 Q2 = 65.5 ; Q3 = 71.75

IQR = Q3 - Q1 = 71.75 - 61.25 = 10.5

Lower limit: Q1 − 1.5 * (IQR)

61.25 - 1.5(10.5)

61.25 - 15.75 = 45.5 (all values below 45.5)

Upper limit: Q3 + 1.5 * (IQR)

71.75 + 1.5(10.5)

71.75 + 15.75 = 87.5 (all values above 87.5)

Hence, the box and whisker plot summary :

Sample size: 24

Median: 65.5

Minimum: 4

Maximum: 80

First quartile: 61.25

Third quartile: 71.75

Interquartile Range: 10.5

Outlier: 4

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!