91Ó°ÊÓ

The Nielsen Media Research television rating measures the percentage of television owners who are watching a particular television program. The highest-rated television program in television history was the \(M^{*} A^{*} S^{*} H\) Last Episode Special shown on February 28,1983 A 60.2 rating indicated that \(60.2 \%\) of all television owners were watching this program. Nielsen Media Research provided the list of the 50 top-rated single shows in television history (The New York Times Almanac, 2006). The following data show the television net- work that produced each of these 50 top-rated shows. \(\begin{array}{lllll}\mathrm{ABC} & \mathrm{ABC} & \mathrm{ABC} & \mathrm{NBC} & \mathrm{CBS} \\ \mathrm{ABC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{NBC} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{CBS} & \mathrm{ABC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{ABC} \\ \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{NBC} \\ \mathrm{CBS} & \mathrm{CBS} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} \\ \mathrm{FOX} & \mathrm{CBS} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{ABC} & \mathrm{ABC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} \\ \mathrm{NBC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{CBS} \\ \mathrm{ABC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} & \mathrm{ABC}\end{array}\) a. Construct a frequency distribution, percent frequency distribution, and bar graph for the data. b. Which network or networks have done the best in terms of presenting top- rated television shows? Compare the performance of \(\mathrm{ABC}, \mathrm{CBS},\) and \(\mathrm{NBC}\)

Step by step solution

01

Count Network Frequency

Count the number of times each network appears in the list. For the given 50 shows, we have the following counts: - ABC: 16 - CBS: 15 - NBC: 18 - FOX: 1

02

Calculate Percent Frequency

To find the percent frequency, divide the frequency of each network by the total number of shows (50) and multiply by 100.- ABC: \( \frac{16}{50} \times 100 = 32\% \)- CBS: \( \frac{15}{50} \times 100 = 30\% \)- NBC: \( \frac{18}{50} \times 100 = 36\% \)- FOX: \( \frac{1}{50} \times 100 = 2\% \)

03

Construct Frequency and Percent Frequency Distributions

Record the frequency and percent frequency of each network in a tabular form:\[\begin{array}{|c|c|c|}\hline \text{Network} & \text{Frequency} & \text{Percent Frequency} \\hline \text{ABC} & 16 & 32\% \\hline \text{CBS} & 15 & 30\% \\hline \text{NBC} & 18 & 36\% \\hline \text{FOX} & 1 & 2\% \\hline\end{array}\]

04

Construct a Bar Graph

Create a bar graph with the networks on the x-axis and their frequencies or percent frequencies on the y-axis. Each bar will represent a network: - ABC has a bar reaching up to 16 shows or 32%. - CBS has a bar reaching up to 15 shows or 30%. - NBC has a bar reaching up to 18 shows or 36%. - FOX has a very small bar for 1 show or 2%.

05

Analyze and Compare Network Performance

From the percent frequency distribution and bar graph, NBC has the highest percentage of top-rated shows at 36%, followed by ABC at 32%, CBS at 30%, and FOX with 2%. Therefore, NBC has done the best in terms of presenting top-rated television shows.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Frequency Distribution

Frequency distribution is a way of organizing data so that it becomes easily understandable. Imagine you are looking at a list of TV networks presenting popular shows. This list is a bit chaotic with repeated names. To make sense of it, you count how many times each network appears. This count for each network is their frequency.

For example, if ABC appears 16 times, CBS 15 times, NBC 18 times, and FOX only 1 time in the list, you have now transformed raw data into a clean, organized set. Frequency distribution helps to simplify the data by showing you clearly which network has the most top-rated shows and which has the least.

In summary, a frequency distribution is a vital tool in statistics that helps you understand the frequency of occurrence of different items in a data set. It's like taking a scattered box of puzzles and putting them into neat categories so you can see the picture more clearly.

Percent Frequency

Once you have a frequency distribution, you might want to know what percentage of the total each frequency represents. This is where the concept of percent frequency comes into play. Percent frequency shows you the relative importance or share of each category as part of the total.

To calculate it, you take the frequency of a category, divide it by the total number, and then multiply by 100 to convert it into a percentage. For instance, if NBC has 18 top-rated shows out of a total of 50, you calculate \( \frac{18}{50} \times 100 = 36\% \).

Percent frequency provides insight into how significant each network is relative to the whole picture. It makes it easier to compare different networks by showing not just the count but also the proportion. This is crucial when you want to quickly understand the distribution of a group or compare the performance of different entities.

Bar Graph

Bar graphs are graphical representations of data that use bars to show how much each category stands for. They are one of the most straightforward and popular ways to visualize frequency distributions.

In the context of our exercise, you have networks on the x-axis (ABC, CBS, NBC, and FOX) and their frequencies or percent frequencies on the y-axis. Each bar's height corresponds to the count or percentage, giving you a visual snapshot of how each network is performing.

Bar graphs are great because they make data comparison easy at a glance. When creating or looking at a bar graph, it's simple to see things like NBC has the tallest bar in our example, meaning they lead in top-rated shows. Meanwhile, FOX has a very short bar, indicating their smaller share.

In essence, bar graphs transform complex numerical data into a clear, comparative format, allowing quick assessments and better decision-making based on the visual insights they provide.