E35: FTCE | General Knowledge | Mathematics | Statistics (Mean, Median, Mode) and More!

0:00:00
Welcome to episode 35 of FTCE seminar, a teacher certification podcast. I'm your host, Mercedes Musto. Today, we'll be having a math conversation about data analysis and statistics to help you prepare for the FTCE general knowledge mathematics subtest. That's right, more math.

0:00:19
And in today's episode, we are diving into the fundamental concepts of measures of central tendency and variability. Well, and how to interpret them in real world context. Whoa, whoa, I know, right? Let's set the stage. Imagine your face with a data set filled with numbers, of course.

0:00:41
But then you're tasked with understanding what those numbers are telling you about the particular situation. This is where measures of central tendency and variability come into play. Let's start with measures of central tendency. These are statistics that represent the center or average of the data set. You may be familiar with the most three common measures of central tendency, and that's the mean, median, and mode.

0:01:08
Now, the mean is simply the average of all the numbers in the data set. To calculate it, you're going to add up all the numbers and then divide by the total count. For example, if you have a data set of test scores, and those scores are 70, 80, 85, and 90, you're going to add them up. 70 plus 80, 85 plus 90, that equals 325, and there's four so divided by four. Since your data set has the four scores, that would give you a mean of 81.25. Remember, mean means average.

0:01:50
Sweet, you got it. Next, the median. The median is the middle value of the data set when it's ordered from smallest to largest. If there's an even number of values, you're gonna take the average of the two middle numbers. For instance, in the data set we just use, 70, 80, 85, and 90 has four numbers.

0:02:12
That makes it an even set. Therefore, the median would be 80 plus 85 divided by 2, 82.5 because it's the average of the middle two numbers, 80 and 85. Lastly, is the mode. The mode is interesting because it's the value that appears most frequently in the data set. In a simple data set of four, seven, seven, eight, and seven, one number occurs more frequently than others. And that's right, it's seven. Therefore, seven is the mode. Now let's talk about measures of variability, which tell us how spread out the data points are.

0:02:54
Two common measures of variability are range and standard deviation. Range is the simplest measure of variability because basically it's the difference between the largest and smallest values in a data set. For example, in the data set of the test scores ranging from 70 to 90, we would subtract the largest from the smallest. So that would be 90 minus 70. That would make the range of this data set 20. Standard deviation on the other hand,

0:03:22
measures the average distance of each data point from the mean. Oh, pop quiz. What's the mean and how do you calculate it? Yes, I knew you were listening. The mean is the average and we calculate it by adding up all the numbers and dividing by the total count.

0:03:39
God, you're doing so awesome. Okay, where were we? Oh, yes, standard deviation. A higher standard deviation indicates that the data points are spread out over a wider range of values, while a lower standard deviation suggests that the data points are closer to the mean. Think of it this way. A higher standard deviation might indicate greater variability in student performance,

0:04:04
whereas a lower standard deviation may suggest more consistency. Hmm, I know, it's a bit more complicated than that, but for the purpose of the test, you will need to understand the terms of central tendency and variability. So how do we interpret these measures in real world context?

0:04:25
Let's go back to our data set with the test scores example. If the mean score is 81.25, does that mean that the mean that a student scored 81.25? No, the mean is the calculated average of the given data set was 70, 80, 85, and 90, and 81.25 represents the average or the mean. This is a good place to discuss range. How do we calculate the range of the data set? 70, 80, 85, and 90? Think about it, range, range.

0:05:08
Oh, range is when we take the difference between the highest and the lowest. Yes, that's correct. Let's review. Measures of central tendency and variability are essential tools for understanding and interpreting data. Remember, common measures of central tendency

0:05:24
are mean, median, and mode. And common measures of variability are range and standard deviation. Being able to identify and understand the difference between mean, median, mode, range, and standard deviation provides you with valuable insights into the characteristics of the data sets you will encounter on the FTCE Math Subtest. For more practice with math concepts, visit ftceseminar.com to study for the test.

0:05:55
The important thing is to start studying and start studying today so you can pass the teacher certification exam. Well, what are you waiting for? Check us out on YouTube at FTCE seminar and start studying today. This podcast was recorded at the Pickens Multimedia Studio at the University of West Florida. This podcast is listener supported. Contributions can be made via the listener support link on Spotify. This is your host Mercedes Musto.

0:06:21
Join me again on FTCE seminar, a teacher certification podcast so you can pass the FTCE.

Transcribed with Cockatoo