# What is the relationship between gaps and outliers in math In this lesson you will learn how to identify clusters, peaks and gaps and their relationship to the data by examining the distribution on a dot plot. Outliers; Features of distributions; Using stem and leaf plots as graphs A stem and leaf plot is used to organize data as they are collected. .. The results of 41 students' math tests (with a best possible score of 70) are recorded below: The result of 4 could be an outlier, since there is a large gap between this and the next. Houghton Mifflin Math: Grade 6. Teaching Models. Graph Data. Collecting and organizing data in a useful way allows students to incorporate Clusters, Gaps, and Outliers A cluster is formed when several data points lie in a small interval.

A line plot of this data set would have "x" marks for temperatures between 50 and 70 and again between 80 andbut there would be nothing between 70 and Researchers can dig deeper and explore why certain data points do not show up in a collected sample.

Isolated Groups Clusters are isolated groups of data points.

• Clusters, gaps, peaks, and outliers
• Outliers in scatter plots

Line plots, which are one of the ways to represent data sets, are lines with "x" marks placed above specific numbers to depict their frequency of occurrence in the data set.

A cluster is depicted as a collection of these "x" marks in a small interval or data subset. For example, if the exam scores for a class of 10 students are 74, 75, 80, 72, 74, 75, 76, 86, 88 and 73, the most "x" marks on a line plot would be in the to score interval.

## Clusters, gaps, peaks & outliers

This would represent a data cluster. Note the frequency for 74 and 75 is two, but for all other scores, it is one. Sciencing Video Vault At the Extremes Outliers are extreme values -- data points that lie significantly outside other values in a data set.

An outlier must be significantly less than or greater than the majority of numbers in a data set. The definition of "extreme" depends on the circumstance and a consensus of the analysts involved in the research. Outliers might be bad data points, also known as noise, or they might contain valuable information about the phenomenon being investigated and the data collection methodology itself. I do have a data point here that is at the high end and I have another data point here that's at the low end, but I don't have any data points that are sitting far above or far below the bulk of the data.

If I had a data point that was out here, then yeah, I would say that was an outlier to the right, or a positive outlier, if I had a data point way to the left off the screen over here, maybe that would be an outlier, but I don't really see any obvious outliers.

All of the data, it's pretty clustered together.

## Identify clusters, peaks and gaps in a dot plot

So I would not say that the distribution has an outlier. The distribution has a peak at 22 degrees. Yeah, it does indeed look like we have, and let's just look at what we're actually measuring: So it does indeed look like we have the most number of days that had a high temperature at 22, most number of days in July had a high tempurature at 22 degrees Celsius, so that is a peak.

You can see it, if you imagine this as kind of a mountain this is a peak right here, this is a high point. You have, at least locally, the most number of days at 22 degrees Celsius.

Judging outliers in a dataset - Summarizing quantitative data - AP Statistics - Khan Academy

So I would say it definitely has a peak there. Since I selected something, I'm not gonna select none of the above. Let's do a couple more of these. Which of the following are accurate descrptions of the distribution below? So the first one, the distribution has an outlier. So, let's see, the lowest They have no days No days where he had between zero and 19 guests, no days where he had between 20 and 39 guests, looks like there's about nine days where he had between 40 and 59 guests, looks like 20 days where he had between 60 and 79 guests, all the way where it looks like maybe 8 days that he had between and guests.

But the question of outliers, there doesn't seem to be any day where he had an unusual number of guests. There's not a day that's way out here, where he had, like, guests. So I would say this distribution does not have an outlier. The distribution has a cluster from zero to 39 guests.

### What Are Gaps, Clusters and Outliers in Math? | Sciencing

So zero to 39 guests is right over here, zero to 39 guests. And there is no days where he had between zero and 39 guests neither zero to 19, or 20 to So there's definitely not a cluster there.

I would say that the cluster would be between days that had between 40 and guests. Definitely not zero and 39, there was no days that were between zero and 39 guests. So I would say none of the above very confidently. Let's do one more of these. The distribution has a peak from 12 to 13 points. Let me see what this is measuring, what this data is about. Test scores by student in Mrs. So you had one student who got between a zero and a one on a point scale, so got between, I guess out of 20 questions, got between zero and one point.