/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 In Pennsylvania the numbers of t... [FREE SOLUTION] | 91Ó°ÊÓ

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In Pennsylvania the numbers of teacher strikes for the last 14 years are shown. Construct a dotplot for the data. Comment on the graph. $$ \begin{array}{rllllrl} 9 & 13 & 15 & 7 & 7 & 14 & 9 \\ 10 & 14 & 18 & 7 & 8 & 8 & 3 \end{array} $$

Short Answer

Expert verified
The dotplot visualizes clustered teacher strikes mostly between 7 and 15, with the most strikes being 18 and a low outlier at 3.

Step by step solution

01

Understand the Data

Identify and list the numbers of teacher strikes for the last 14 years as provided: 9, 13, 15, 7, 7, 14, 9, 10, 14, 18, 7, 8, 8, 3.
02

Organize the Data

Sort the numbers in ascending order: 3, 7, 7, 7, 8, 8, 9, 9, 10, 13, 14, 14, 15, 18.
03

Construct the Dotplot

On a number line ranging from 3 to 18, place a dot above each number for every occurrence in the data. For instance, above the number 7, place three dots as it appears three times.
04

Describe the Dotplot

The dotplot shows the distribution of teacher strikes over 14 years, with most values clustering between 7 and 15. A single outlier is at 3, and the highest number of strikes is 18.

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Key Concepts

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

Data Visualization
Data visualization is a powerful tool used to present numerical data in a visual format, making it easier to see patterns, trends, and outliers. One popular form of data visualization is the dotplot. Dotplots are simple yet effective visualizations that use dots to represent frequency. They allow for quick insights into the distribution of data points.
When constructing a dotplot, each dot represents one occurrence of a data point. The data is organized along a number line. This method helps in identifying the shape and spread of the data. For example, in our dotplot of teacher strikes, a clear clustering of dots can often be observed, indicating the most frequent occurrences.
Dotplots are particularly useful for small datasets, and they provide a straightforward way to compare frequencies across different values. This makes them excellent for detecting gaps, clusters, and outliers, offering a clear visual summary of how data is distributed.
Descriptive Statistics
Descriptive statistics are numbers that summarize and describe the characteristics of a dataset. They provide simple summaries about the sample and the measures. Key descriptive statistics include mean (average), median (middle value), and mode (most frequent value).
For the dataset of teacher strikes, calculating these statistics can offer valuable insights. For example:
  • The mean gives us the average number of strikes per year, providing a central tendency.
  • The median shows the middle value when data is organized in ascending order, offering another measure of central tendency which is often more robust against outliers than the mean.
  • The mode indicates the most frequently occurring number of strikes, in this case, it’s 7, as it appears three times in the dataset.
The range, another important statistic, highlights the difference between the highest and lowest values in the dataset. This helps in understanding the spread of the strikes over the years.
Teacher Strikes Analysis
Analyzing teacher strikes using data visualization and descriptive statistics helps uncover patterns and trends over time. This kind of analysis can reveal insights into the frequency and intensity of strikes, which might relate to various socioeconomic factors.
In this context, a dotplot shows a concentration of strikes between 7 and 15 per year, with an unusual low at 3 and a high of 18 strikes. Such a visual representation can prompt further investigation into why certain years had higher or lower strike numbers.
The patterns observed might lead stakeholders to explore correlating factors such as economic conditions, policy changes, or negotiation outcomes. Detecting whether any external events correlate with these spikes or dips might help in formulating strategies to minimize disruptions caused by future strikes.
This analytical approach supports not only educational administrators but also policymakers in understanding historical strike trends, potentially guiding future decisions towards more sustainable labor practices.

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Most popular questions from this chapter

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Eating at Fast Food Restaurants A survey was taken of 50 individuals. They were asked how many days per week they ate at a fast-food restaurant. Construct a frequency distribution using 8 classes \((0-7) .\) Based on the distribution, how often did most people eat at a fastfood restaurant? $$ \begin{array}{lllll} 1 & 3 & 4 & 0 & 4 \\ 5 & 2 & 2 & 3 & 1 \\ 2 & 2 & 2 & 2 & 2 \\ 2 & 2 & 2 & 2 & 3 \\ 2 & 2 & 5 & 2 & 4 \\ 2 & 4 & 5 & 2 & 1 \\ 4 & 1 & 3 & 2 & 2 \\ 2 & 0 & 7 & 2 & 3 \\ 2 & 2 & 2 & 5 & 2 \\ 3 & 3 & 4 & 1 & 3 \end{array} $$

Average Wind Speeds A sample of 40 large cities was selected, and the average of the wind speeds was computed for each city over one year. Construct a frequency distribution, using 7 classes. \(\begin{array}{rrrr}12.2 & 9.1 & 11.2 & 9.0 \\ 10.5 & 8.2 & 8.9 & 12.2 \\ 9.5 & 10.2 & 7.1 & 11.0 \\ 6.2 & 7.9 & 8.7 & 8.4 \\ 8.9 & 8.8 & 7.1 & 10.1 \\ 8.7 & 10.5 & 10.2 & 10.7 \\ 7.9 & 8.3 & 8.7 & 8.7 \\ 10.4 & 7.7 & 12.3 & 10.7 \\ 7.7 & 7.8 & 11.8 & 10.5 \\\ 9.6 & 9.6 & 8.6 & 10.3\end{array}\) Source: World Almanac and Book of Facts.

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