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

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

chiken

step-by-step explanation: