Chapter 3: Problem 4
In order to find the median of a data set, what do we do first with the data?
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 3: Problem 4
In order to find the median of a data set, what do we do first with the data?
These are the key concepts you need to understand to accurately answer the question.
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Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by \(10 .\) (a) Does the mean change? Explain. (b) Does the median change? Explain. (c) Is it possible for the mode to change? Explain.
The town of Butler, Nebraska, decided to give a teacher-competency exam and defined the passing scores to be those in the 70 th percentile or higher. The raw test scores ranged from 0 to \(100 .\) Was a raw score of 82 necessarily a passing score? Explain.
Expand Your Knowledge: Harmonic Mean When data consist of rates of change, such as speeds, the harmonic mean is an appropriate measure of central tendency. For \(n\) data values, $$\begin{aligned} \text { Harmonic mean } &=\frac{n}{\sum \frac{1}{x}}, \text { assuming no data value is } 0 \end{aligned}$$ Suppose you drive 60 miles per hour for 100 miles, then 75 miles per hour for 100 miles. Use the harmonic mean to find your average speed.
Merit Pay Scale: Weighted Average At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients. Then an average is determined by giving a weight of 2 for promptness, 3 for record keeping, 1 for appearance, and 4 for bedside manner with patients. What is the average rating for a nurse with ratings of 9 for promptness, 7 for record keeping, 6 for appearance, and 10 for bedside manner?
If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of \(x\) values. The sample size is \(n .\) Fill in the details for the following steps. $$\begin{aligned} \Sigma(x-\bar{x})^{2} &=\Sigma x^{2}-2 \bar{x} \Sigma x+n \bar{x}^{2} \\ &=\Sigma x^{2}-2 n \bar{x}^{2}+n \bar{x}^{2} \\ &=\Sigma x^{2}-\frac{(\Sigma x)^{2}}{n} \end{aligned}$$
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