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Chapter 2: Problem 54

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right. What word describes a distribution that has two modes?

Short Answer

Expert verified
The distribution is called bimodal.

Step by step solution

01

Understanding the Problem

We need to determine the term used to describe a distribution with certain characteristics, specifically when it has two modes.
02

Define a Mode

A mode is the value or values that appear most frequently in a data set. A single set of data might have one mode, more than one mode, or no mode at all.
03

Identify Distribution with Two Modes

A distribution with two modes is called a bimodal distribution. This means that there are two different values that occur with the highest frequency.

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Key Concepts

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

Mode
The mode is an essential concept in statistics that refers to the number that appears most frequently in a data set. Understanding the mode helps in identifying trends and patterns within data. In simple terms, the mode is like the most popular choice in a group of numbers.
Among datasets, there might be one mode, also known as unimodal, more than one mode, or no mode at all. For example:
  • If you have the numbers 2, 3, 4, 4, 5, the mode is 4, since 4 appears more often than any other number.
  • In a dataset like 2, 2, 3, 3, 4, the modes are 2 and 3, making it a bimodal distribution.
  • There could also be no mode if no number is repeated more than once.
Recognizing whether a dataset has a mode or multiple modes is useful in understanding its nature and finding patterns.
Statistical Distribution
In statistics, a distribution describes the way values are spread out across a dataset. A statistical distribution shows how data points are distributed over values or intervals. Understanding distribution is critical for knowing how data behaves.
There are several types of distributions:
  • Normal Distribution: Often known as a bell curve, where most values cluster around the central point, and symmetrically lessen as they move away.
  • Uniform Distribution: Each value has an equal chance of occurring.
  • Skewed Distribution: Data tends to tail off in one direction, either left or right.
Each distribution has its unique properties and applications depending on data behavior and research goals.
Data Symmetry
Data symmetry in a statistical distribution refers to how a dataset is mirrored around its center point. Symmetrical data is balanced on both sides of its central value鈥攍ike a mirror image.
The most common example is the normal distribution, which is perfectly symmetrical. In a normal distribution, each side is a mirror image of the other, with most data points concentrated around the central mean.
On the other hand, skewed data lacks this balance:
  • Left-Skewed (Negatively Skewed): The tail on the left side is longer or fatter.
  • Right-Skewed (Positively Skewed): The tail on the right side is elongated.
Identifying symmetry or skewness is important for interpreting data correctly and choosing the appropriate statistical methods.
Frequency Distribution
A frequency distribution provides a detailed view of how often each value in a dataset occurs. It offers a glance at the concentration of data points by tallying occurrences.
  • Frequency Table: A table that charts the number of times each data point appears.
  • Histogram: A bar graph that visually represents frequency, allowing quick assessments of data spread and concentration.
A frequency distribution helps identify patterns such as the mode, ranges of data, and how distributed values compare with each other. By exploring frequency distributions, you can spot trends and essential insights hidden within complex datasets, revealing their behaviors and any irregularities.

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Most popular questions from this chapter

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right. 1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain.

a. For runners in a race, a higher speed means a faster run. Is it more desirable to have a speed with a high or a low percentile when running a race? b. The 40th percentile of speeds in a particular race is 7.5 miles per hour. Write a sentence interpreting the 40th percentile in the context of the situation.

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