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Chapter 3: Problem 19

Use the following cell phone airport data speeds (Mbps) from Sprint. Find the percentile corresponding to the given data speed. $$\begin{array}{cccccccccc} 0.2 & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 & 0.3 & 0.4 & 0.4 & 0.4 \\ 0.5 & 0.5 & 0.5 & 0.5 & 0.5 & 0.6 & 0.6 & 0.7 & 0.8 & 1.0 \\ 1.1 & 1.1 & 1.2 & 1.2 & 1.6 & 1.6 & 2.1 & 2.1 & 2.3 & 2.4 \\ 2.5 & 2.7 & 2.7 & 2.7 & 3.2 & 3.4 & 3.6 & 3.8 & 4.0 & 4.0 \\ 5.0 & 5.6 & 8.2 & 9.6 & 10.6 & 13.0 & 14.1 & 15.1 & 15.2 & 30.4 \end{array}$$ $$0.7 \mathrm{Mbps}$$

Short Answer

Expert verified
0.7 Mbps is at the 36th percentile.

Step by step solution

01

Organize the Data

The given data speeds are already listed in an ascending order. This makes it easier to find ranks and percentiles.
02

Identify the Rank

Identify the rank (position) of the data speed 0.7 Mbps in the ordered list. The rank for 0.7 Mbps is 18.
03

Apply the Percentile Formula

Use the formula for the percentile: \[ P = \frac{n}{N} \times 100 \] where \( n \) is the rank and \( N \) is the total number of observations (data points).Here, \( n = 18 \) and \( N = 50 \).
04

Calculate the Percentile

Substitute the values into the formula: \[ P = \frac{18}{50} \times 100 = 36 \] So, the 0.7 Mbps data speed corresponds to the 36th percentile.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentile Rank
The percentile rank is a way to understand the relative standing of a value within a dataset. It's the percentage of data points that are equal to or less than a particular value.

To find the percentile rank, you need to:
  • Organize the data in ascending order.
  • Determine the rank (or position) of the value in the dataset.
  • Use the percentile formula to calculate the rank's percentile.
In the given example, the data speed of 0.7 Mbps is in the 18th position out of 50 total data points. This position is then converted into a percentile using the formula.
Statistical Data Organization
Organizing data is the first essential step in many statistical calculations, including finding percentiles. Proper organization helps in easy interpretation and analysis.

Here are some key points:
  • Data should be listed in ascending order.
  • Orderly data makes it easy to find measures of central tendency (like median) and dispersion (like range).
  • It aids in identifying patterns and outliers in the dataset.
In our given problem, the cell phone airport data speeds are already sorted. This step facilitates the next steps of identifying the rank and applying the formula. When data is not organized, it can lead to incorrect calculations and results.
Percentile Formula
The percentile formula is used to convert the rank of a value into its percentile rank. The formula is:

< <
calculate the percentile rank.
ensure
Our calculation looked like this:
In summary, 0.7 Mbps data speeddings.

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Most popular questions from this chapter

Consider a value to be significantly low if its \(z\) score is less than or equal to -2 or consider the value to be significantly high if its \(z\) score is greater than or equal to \(2 .\) Designing Aircraft Seats In the process of designing aircraft seats, it was found that men have hip breadths with a mean of \(36.6 \mathrm{cm}\) and a standard deviation of \(2.5 \mathrm{cm}\) (based on anthropometric survey data from Gordon, Clauser, et al.). Identify the hip breadths of men that are significantly low or significantly high.

Watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, \((d)\) midrange, and then answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. What do the results tell us? \(\begin{array}{rrrrrrrrrrr}89 & 91 & 55 & 7 & 20 & 99 & 25 & 81 & 19 & 82 & 60\end{array}\)

Find the mean and median for each of the two samples, then compare the two sets of results. Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 "Body Data" in Appendix B). Does there appear to be a difference? $$\begin{array}{llllllllllll}\text { Male: } & 86 & 72 & 64 & 72 & 72 & 54 & 66 & 56 & 80 & 72 & 64 & 64 & 96 & 58 & 66 \\\\\text { Female: } & 64 & 84 & 82 & 70 & 74 & 86 & 90 & 88 & 90 & 90 & 94 & 68 & 90 & 82 & 80\end{array}$$

Find the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (Exercise 29) 36.2 years; (Exercise 30) 44. I years; (Exercise 31) 224.3; (Exercise 32) 255.I. $$\begin{array}{|c|c|}\hline \begin{array}{c}\text { Blood Platelet Count of } \\\\\text { Males }(1000 \text { cells } / \mu L)\end{array} & \text { Frequency } \\\\\hline 0-99 & 1 \\ \hline 100-199 & 51 \\\\\hline 200-299 & 90 \\\\\hline 300-399 & 10 \\\\\hline 400-499 & 0 \\ \hline 500-599 & 0 \\\\\hline 600-699 & 1 \\\\\hline\end{array}$$

If your score on your next statistics test is converted to a \(z\) score, which of these \(z\) scores would you prefer: \(-2.00,-1.00,0,1.00,2.00 ?\) Why?
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