/*! 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 21 Find the mode for the sample com... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 21

Find the mode for the sample composed of the observations \(4,5,6,6,6,7,7,8\)

Short Answer

Expert verified
The mode of the sample composed of the observations \(4, 5, 6, 6, 6, 7, 7, 8\) is \(\boxed{6}\), as it appears with the highest frequency (3 times).

Step by step solution

01

Identify distinct observations

First, identify all unique values in the dataset: \(4, 5, 6, 7, 8\).
02

Count the frequency of each distinct observation

Now count the frequency of each distinct observation in the sample: - \(4\) appears \(1\) time. - \(5\) appears \(1\) time. - \(6\) appears \(3\) times. - \(7\) appears \(2\) times. - \(8\) appears \(1\) time.
03

Identify the mode

The mode is the observation with the highest frequency. In this case, \(6\) has the highest frequency (appearing \(3\) times). So the mode of this sample is \(\boxed{6}\).

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.

Frequency Distribution
In statistics, a frequency distribution serves as a helpful tool to organize data. It details how often each value in a dataset appears. When you categorize or tally data this way, it becomes much easier to see patterns and make observations.

A frequency distribution breaks down the dataset into distinct values and then notes the frequency (or count) of each.
  • If you had a dataset containing numbers that represented shoe sizes, for example, you could organize them by each shoe size and how often each size appears.
  • This helps in understanding the most common sizes and any outliers or unusual sizes.
In the context of our example, the frequency distribution is given by the counts of each observation:
  • The number \(4\) appears \(1\) time.
  • The number \(5\) appears \(1\) time.
  • The number \(6\) appears \(3\) times.
  • The number \(7\) appears \(2\) times.
  • The number \(8\) appears \(1\) time.
Recognizing the frequency of each occurrence allows statisticians to further analyze the dataset for additional insights.
Statistical Observation
Statistical observation involves carefully looking at the data you've collected, noting patterns or trends, and using this information to find answers. It's essential for identifying not just frequencies but any interesting or unusual patterns in the dataset.

A good statistical observation is key to identifying the mode, which is the most frequently occurring value in a dataset. This involves observing not only individual numbers but also their repetition across the data.
  • For instance, in our previous exercise, observing that the number \(6\) occurs \(3\) times while other numbers occur less frequently helped us identify it as the mode.
  • Such observations allow for a better understanding of typical behaviors or outcomes within a dataset.
Robust statistical observation is the backbone of any data analysis, forming the groundwork for deeper statistical analysis or predictions.
Distinct Values
Distinct values in a dataset are the individual, unique entries within the data. They stand out because each one only needs to appear once for it to be distinct. Identifying these unique values is crucial in understanding the dataset's variety and can influence various statistical measures.

When you identify distinct values, you separate repetitive data to focus only on the unique instances:
  • From a list like \(4, 5, 6, 6, 6, 7, 7, 8\), the distinct values would be \(4, 5, 6, 7, 8\).
  • This makes it easier to construct a frequency distribution, as you then only need to count how often these distinct numbers appear.
Understanding distinct values is particularly important because it helps identify the foundation of your dataset, eliminating any noise created by repeated details. Recognizing these values helps reduce the complexity of data analysis while ensuring important values are highlighted.

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

Consider the distribution of the previous problem. Let us add 2 relatively high values in order to observe the differential effect on the three measures of central tendency. Use the following eight ordered values: \(3,5,6,6,7,9,16,20\).

Find the mean salary for four company employees who make \(\$ 5 / \mathrm{hr}, \$ 8 / \mathrm{hr} ., \$ 12 / \mathrm{hr} .\) and \(\$ 15 / \mathrm{hr}\).

For this series of observations find the mean, median, and mode. \(500,600,800,800,900,900,900,900,900,1000,1100\)

Find the variance of the sample of observations \(2,5,7,9,12\).

The number of home runs the Boston Red Sox hit in eight consecutive games were \(2,3,0,3,4,1,3,0\). (a) What is the mean number of home runs hit? (b) What is the median? (c) What is the mode?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.