DENTISTRY To study the effect of fluoride in preventing...

Key Concepts

Class Intervals

Class intervals, or bins, are ranges into which data is grouped when creating a frequency distribution or histogram. Choosing appropriate intervals is essential because they determine how well the histogram represents the underlying data and can affect the interpretation of its distribution.

Histogram

A histogram is a type of bar graph that represents the frequency distribution of a dataset by showing the number of observations that fall within predetermined intervals, known as bins. Histograms are a powerful visual tool in statistics that help in identifying the shape, central tendency, and spread of the data.

Data Visualization

Data visualization is the practice of presenting data in graphical formats, such as histograms, to communicate information clearly and efficiently. This approach makes complex data more understandable, aids in identifying patterns and anomalies, and supports deeper insights during statistical analysis.

Frequency Distribution

A frequency distribution is a method of organizing and summarizing data by dividing it into distinct groups or intervals and then counting the number of observations that fall within each group. This technique is fundamental in statistics for understanding the shape and spread of a dataset and for identifying patterns or trends.

Tally Marks

Tally marks are a simple recording method used to count and represent data quickly, often as the initial step in creating a frequency distribution. They provide an efficient way to manually count occurrences before summarizing them numerically, which is particularly useful during data collection or preliminary analysis.

Transcript

00:01 Okay, we've got a problem about dentistry.

00:05 To study the effect of fluoride in preventing tooth decay, researchers counted the number of fillings in the teeth of 28 patients and recorded these results.

00:15 So each one of those numbers, 3, 7, 11, 21, etc., represent the number of fillings some person had.

00:24 So some person had 3 fillings, some person had 7.

00:26 Some poor soul had 21 fillings.

00:29 Oh, i feel sorry for them.

00:30 I don't like to get fillings.

00:32 And so we're going to make a histogram.

00:35 So we're going to tally the results.

00:38 And they didn't give me the table here, but we'll figure it out.

00:46 And so our ranges, remember with a histogram, we look at the ranges, and then we count how many are in the range.

00:57 So like down here i've got this 0 .5 to 5 .5 that would be a range so that that's the range of having half a cavity to 5 .5 cavities now we know that's not possible but that's the range and i'm going to count all the people who had cavities in between 0 .5 and 5 .5 so that would have been 1 2 3 4 and 5 so i'm going to count all the people the number of people that had either either one cavity, two cavities, three cavities, four cavities, or five cavities.

01:28 And i'm going to write some number there, and then we're going to use that number later on to draw a histogram.

01:36 So we're going to make a bar the height of the number of people that fell into these categories.

01:43 We'll continue this process with each new range of values all the way up to 25 .5.

01:52 So now what i'm going to do well actually what i've already done because i didn't think you wanted to listen to me do it is i took these values and i lined them up in order so i said well okay we got a two here so i started with two and then i found a couple of threes so i'm trying to put them in order from smallest to biggest so it's easier to see where they go now you don't have to do that you may just go through and make tally marks but i just thought we would do that so i've written them i've written them on the next page and we're gonna use colors so i don't have to tally so i'm gonna start with red and i'm gonna go over here and i'm going from i'm starting with 0 .5 to 5 .5 so i'm looking for the number of the number of cavities between basically one and five so there's one there's one there's one so this is our red range so there were three total let's see the next one is five point five to ten so we're looking at who had cavities that six cavities seven cavities eight cavities nine nine cavities, or ten cavities.

03:15 So we're going to use blue.

03:17 Okay, so seven, eight.

03:19 So these are in between all the way up to ten, but not going past ten.

03:25 So that's our next category, and it looks like, let's see.

03:29 So in this one, there were three.

03:32 In this one, how many are there? one, two, three, four, five, six, seven.

03:38 So there's seven.

03:39 I'll make a little seven right there to remember.

03:41 Okay, what's our next one? our next one is green.

03:46 It's going to be basically 11 through 15 cavities.

03:51 So we'll go green and we're going to do 11 through, what did i say? 15...