When using histograms to compare two data sets, it is...

When using histograms to compare two data sets, it is sometimes difficult to make comparisons by looking back and forth between the two histograms. A back-to-back relative frequency histogram has a format that makes the comparison much easier. Instead of frequencies, we should use relative frequencies (percentages or proportions) so that the comparisons are not difficult when there are - different sample sizes. Use the relative frequency distributions of the ages - of Oscar-winning actresses and actors from Exercise 15 in Section $2-2,$ and complete the back-to-back relative frequency histograms shown below. Then use the result to compare the two data sets.

Key Concepts

Histogram

A histogram is a graphical representation of the distribution of numerical data, where data is grouped into bins or intervals and the frequency of data points within each bin is represented by the height of a bar. It helps to visualize the shape, spread, and central tendency of a data set.

Relative Frequency

Relative frequency converts the raw counts in each bin of a histogram into proportions or percentages, which makes it possible to compare distributions accurately even when the total number of observations in different samples vary.

Back-to-back Histogram

A back-to-back histogram is a specialized type of histogram used to compare two data sets side by side, with the bars for one data set extending in one direction and the bars for the other extending in the opposite direction. This format facilitates direct visual comparison of the distributions, highlighting differences in patterns or central tendencies between the two groups.

Transcript

00:01 Number 19 gives you quite a bit of information to start with.

00:05 So you can see here that on this side over here, we actually have some data from a previous question that they asked you to use.

00:15 In particular, we are looking at histograms from exercise 15 in section 2, and we actually found all of those charts during that question.

00:26 Then they give you this guy over here, which is a back -to -back relative frequency histogram, where your x -axis is now actually in the middle, and your y -axis is right here for the one graph and here for the other.

00:43 But you can see that they both start in the middle at zero and then move their way away from that middle point as they get higher.

00:54 Now, the reason they do this is because it's going to make it a bit easier for us to compare the two graphs once it's all done.

01:02 Now, they do actually go ahead and start these two graphs for us, but they're going to ask us to finish these graphs and then go ahead and compare the two.

01:12 It should be noted that these over here are the female ages, and on the right hand side, we have our male ages.

01:22 So these are the age of best actress when they won an oscar.

01:28 And let's go ahead and spread this.

01:29 So for females, they already knocked out the 32 and the 41.

01:34 So our next range here from the 40 to 49 goes up to 15 .6.

01:40 15 .6 would be about halfway between that 10 and 20.

01:46 So there would be our bar there.

01:49 Then for our next one, we're just looking at a 2 .4, so that's way low.

01:56 Probably even that was a little high.

01:59 Make that a bit shorter.

02:04 Then from the 50 to 59 range, we are going to be looking at 2 .4.

02:14 Oh, wait, that's actually one we just did.

02:17 So the 4 .9 is our next one from 60 to 69.

02:19 So 4 .9 is going to be a little bit further than the last one.

02:24 Double that.

02:28 And then we need to do two 1 .2s, which will be hardly slivers in this case, just because they're not going to be making it very far off that zero.

02:39 So this is kind of the total histogram here.

02:42 You can color this in to be a little bit better to match the rest of their graph that they have here.

02:48 But that's going to be the histogram for the relative frequency histogram for the field.

02:52 Now if we want to move on to the males, we do the same thing.

02:55 They already did the 1 .2 there.

02:57 You can see their little sliver down here.

03:00 Then they're going to go ahead.

03:01 Next one we've got to jump up to is the 31...