Comparing distributions using summary statistics

0:00- [Instructor] The table shows summary statistics for daily temperature in degrees Fahrenheit in two cities based on a hundred days each. Which city is hotter on average? So pause this video and have a go at that. All right, so typically when people say average in everyday language, they're usually talking about the mean.

0:18In statistics sometimes average can refer to any measure of central tendency. So sometimes people might even say, "Well, median is a way of measuring average," but let's just look at the data, or at least the statistics here, and see which one is looking hotter.

0:32So Sunvale has a higher mean than Lakeburg, and it has a higher median. So to me, I feel that Sunvale is clearly, regardless of how you define average, but especially if you take the typical definition of average, but even if you think about the median, either way, if you look at these measures of central tendency, Sunvale is hotter.

0:56So Sunvale, because its standard deviation is larger. No, that would just mean you had a lot more variation. Sunvale, because it's mean and median temperatures are higher. Yes, I like that choice and we know it's not Lakeburg. Let's do another example. The table shows summary statistics for two printer models tested for printing speed in pages per minute.

1:19All right, Issa claims that SpeedPro X printers are faster and are more consistent in printing speed. Do the summary statistics support Issa's claim? And you could have a go at this one as well. Okay, so let's look at these measures of central tendency. When people tend to say faster, well, faster could be median or mean.

1:42But let's see, when we look at this right over here, speed, this is the number of pages per minute. So the more pages per minute, the faster you are. So SpeedPro is definitely by, when you look at the mean, it looks like it is faster. The median is about, is actually the same number.

2:02But when I take both of these together, I would still give it to SpeedPro because if you take just the traditional mean, which most people talk about when they talk about average, it's definitely faster. And then Issa also claimed more consistent. So more consistent would mean smaller range, smaller variation, smaller standard deviation.

2:23And we could see that's definitely the case with SpeedPro. Its range is six versus JetPrint 200 at 10, its standard deviation is two versus JetPrint 200 at three. So yes, let's see. So it's yes, because SpeedPro X has a smaller range and standard deviation, and that means it must also be faster.

2:44No, the range and standard deviation are good for our consistency, but let's see. Yes, because SpeedPro X has a larger mean. Yes, that's more pages per minute, a smaller range in standard deviation. So it's faster and more consistent. Yeah, I like that one. Let's see, no, because JetPrint 200 has a larger mean.

3:01We just know that that's not true. JetPrint 200 does not have a larger mean. And then the last one, no, because the medians are the same for both models so SpeedPro X cannot be faster, even though it is more consistent. If all they gave was the median, if all they gave was the median information that you, I might have been tempted to pick D, but they gave us the mean information and for me that's the tiebreaker here, where it is faster, especially in everyday language.

3:30It's definitely more pages per minute mean or on average in everyday language. So I would give the tip to SpeedPro X.