in this video we will be talking about bar charts pie charts histograms stem plots and time plots we can use these tools as a way of displaying data we often use bar charts and pie charts to display categorical data and we often use stem plots time plots and histograms for displaying quantitative data pie charts show the relative size of each value in relation to the whole on the other hand bar charts display the frequency on one axis and the values of the categorical variable on the other you can think of bar charts as a way
of tallying information for quantitative data we often use stem plots histograms and time plots to show information we all talk about histograms first after collecting data from a population or sample we can use a histogram to help us display the distribution of the data we collected the frequency or count is displayed on one axis and each count tells us how many data values fall within a predetermined interval on the other axis this axis corresponds to the variable we have just measured to read a histogram you first pick one of the intervals and determine its height
so for the interval between 100 and 110 we see that the bar has a height of 8 this means that from the data we collected 8 people weigh between 100 and 110 pounds for the next interval we see that the bar has a height of 16 so this means that 16 out of the total people I collected data from weigh between 110 and 120 pounds the rest of the histogram can be read in a similar fashion a histogram is a form of a frequency distribution frequency distributions can be written in a table format and they
tell us how many data values fall within a certain interval these intervals can be a little confusing for example if I recorded an individual's weight to be exactly 120 pounds do I include them in this interval or this interval by convention we see that each interval does not include the right endpoint so 120 is not included in this interval and 130 is not included in the other interval so in fact 120 belongs to the second interval now you might be thinking if the right interval isn't included why don't I just rewrite my intervals like this
110 to 119 and 120 to 129 now the problem with this is that we don't have continuity for example if you weighed 119.7 pounds there would be no interval that contains this value now a frequency distribution can be converted into something called a relative frequency distribution the only difference between these two is that a regular frequency distribution shows a count and a relative frequency distribution as the name suggests shows the relative frequency instead it is called relative frequency because it represents the proportion of values in each interval in relation to the whole to convert a
frequency distribution into a relative frequency distribution we will need to do some calculations we start off by finding the total number of data values and we do this by adding each frequency we find that the total sum is equal to 50 then we will take each value and we will divide it by that sum and as a result we get the relative frequency values to check if you have made the right conversions you can add up all the proportions for each interval and the sum should be equal to one the answer should be equal to
one because we have used a ratio that relates our data to the total amount of data values because of this ratio relative frequencies can be written in percentages to convert to percentage form all we do is multiply each value by 100% in the same way regular histograms can converted into histograms that tell us the proportion of values for each interval now stem plots are like histograms except the show each data point stem plots consists of stems and leaves a leaf refers to the very last number and a stem refers to all of the other numbers
except the last number stems and leaves are usually separated by a line for example let's look at the number 117 the leaf is the last number so this would be 7 the stem is all of the other numbers so the stem is 11 on a stem plot this will be written as so now let's look at the number 69 using the same rules we would get a leaf of 9 and a stem of 6 and on a stem plot this would be written as so now when we have a string of leave like this it
just means that I have the data points 30 31 32 35 and 35 notice how stem plots are constructed stems go down from low to high and leaves extend outward from low to high depending on the data set we are working with sometimes we can get stem plots with too many leaves and we can get stem plots with too many stems when this happens we might not get a nice picture of the distribution and as a result we may not be able to get much information out of it if we have a regular stem plot
with too many leaves we can convert it into something called a split stem plot this conversion is called splitting the stems to split the stems we need to duplicate each stem the first stem will run from 0 to 4 which corresponds to these values and the second stem will run from 5 to 9 which corresponds to these values the same logic can be applied to the rest of the stems when we have too many stems we can reduce the amount of stems by trimming the leaves in this example we have a very large data set
that goes from 201 all the way to 875 that's over 60 stems that we have to write to trim the leaves all we do is remove the very last digit so notice for the number 201 the leaf is one and the stem is 20 after removing the very last digit we get 20 so now the leaf becomes zero and the stem is now 2 we would do the same process for each data value by trimming the leaves we get a better-looking stem plop notice how we have reduced the amount of stems by doing this and
we have saved ourselves the trouble of having to write down over 60 stems this is why trimming can be useful but be careful when you read the stem plot after it has been trimmed for example for the top rope instead of reading it as 20 20 21 22 23 and so on we read it as 200 200 210 220 230 and so on this is because the original data was in the hundredths place now the last type of stem plot we will be looking at is called a back-to-back stem plot back to back stem plots
are used to display and compare two distributions by using the same set of stems so for example we could compare data from males and females or data from cats and dogs another way to display quantitative data is by using a time plot time plots show how a variable changes over time by convention time is always plotted on the x-axis and the values of a variable are always plotted on the y-axis
