/*! 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 43 Use the following information to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 43

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40 Calculate the mean.

Short Answer

Expert verified
The mean length of the boats is approximately 27.22.

Step by step solution

01

Summing the Values

Add all the lengths of the boats given in the dataset: 16, 17, 19, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 29, 30, 32, 33, 33, 34, 35, 37, 39, 40. The sum is \(16 + 17 + 19 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 27 + 27 + 27 + 28 + 29 + 30 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 40 = 735\).
02

Counting the Data Points

Count the total number of data points. There are 27 lengths given in the dataset.
03

Calculating the Mean

Divide the total sum of the data points by the number of data points. The mean is calculated as \( \frac{735}{27} = 27.22\) (rounded to two decimal places).

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 91影视!

Key Concepts

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

Understanding Mean Calculation
Calculating the mean, or average, of a dataset is a fundamental aspect of descriptive statistics. The mean gives us a central value that represents the entire dataset. It's one of the most common tools used for summarizing a collection of numbers and is particularly useful when you want to get a quick sense of what a typical value might be.

To calculate the mean, follow these steps:
  • First, add up all the numbers in the dataset, which is known as the sum.
  • Next, count how many numbers are in the dataset. This gives you the total number of data points.
  • Finally, divide the sum by the number of data points. This result is the mean of the dataset.
For example, in our dataset of boat lengths, we summed all the lengths (16, 17, ... 40) to get 735. We then divided the sum by the total number of boat lengths, 27, to get a mean of approximately 27.22.
The Importance of Dataset Analysis
Dataset analysis involves examining and interpreting data to uncover patterns and extract meaningful insights. It allows us to identify underlying trends and make informed decisions.

In the context of our boat length dataset:
  • Starting by ordering the data helps ensure accurate calculations and reveals distribution patterns.
  • The range of values, from the shortest to the longest boat, can give us an idea about variability. Here, the lengths range from 16 to 40.
  • A quick analysis can show us whether our data points are concentrated or spread out across different values.
Performing dataset analysis enables us to grasp the broader picture and see beyond individual numbers. It helps highlight trends like clustering of values around 25 and 27 in our dataset.
Exploring Numerical Data Analysis
Numerical data analysis focuses on using quantitative methods to summarize, analyze, and make conclusions about numerical datasets. It equips us with tools for deeper insight.

Key components of numerical data analysis include:
  • Measures of central tendency, such as the mean, median, and mode, which tell us about the center of the dataset.
  • Measures of variability, like range, variance, and standard deviation, which inform how spread out the data points are.
  • Graphical representations, like histograms or scatter plots, to visualize the data distribution.
In the case of the marina's boat lengths, numerical data analysis enables us to quickly see the average size, notice any outliers, and understand the data's spread. This analysis helps in making predictions or decisions based on the summarized local boating patterns.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the 78th percentile. Should Li be pleased or upset by this result? Explain.

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following: sample mean \(=\overline{x}=\)____

The mean and median for the data are the same. 3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7 Is the data perfectly symmetrical? Why or why not?

For each of the following data sets, create a stem plot and identify any outliers. The data are the prices of different laptops at an electronics store. Round each value to the nearest ten. 249, 249, 260, 265, 265, 280, 299, 299, 309, 319, 325, 326, 350, 350, 350, 365, 369, 389, 409, 459, 489, 559, 569, 570, 610

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following: mode \(=\)____
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.