12. | Expand Your Knowledge: Outliers 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 them 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 soft- ware 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 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) Make a box-and-whisker plot of the data. (b) Find the interquartile range (IQR). (c) Multiply the IQR by 1.5 and find the lower and upper limits. (d) Are there any data values below the lower limit? above the upper limit? List any suspected outliers. What might be some explanations for the outliers?

Q: -0.50 1.00 а) 0.60 -100 -0.50 b) 0.60 100 -1.00 -0.50 1.00 c) 0.60 -1.00 -0.50 1.00 d) 60 -1.00

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.