Graphical Analysis In Exercises 59 and 60, th...

Question

Graphical Analysis In Exercises 59 and 60, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers.

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Accepted Answer

Welcome back, everyone. The histogram below shows the number of vacation days used by employees in a company over the past year. The letters X, Y, and Z are marked at various points on the horizontal axis. Describe the shape of the data distribution and determine which letter X, Y, or Z corresponds to the mean, median, and mode. And here we have our histogram. Now let's take a look at this graph. What can we tell in our initial inspection? Well, we can notice that the histogram shows a right skewed or positively skewed distribution. That's because most employees use a small number of vacation days where fewer employees use a large number of vacation days, and the tail extends to the right, which is a key sign of right SKU. OK? So here we can say then that our distribution. The distribution the data. Is right skewed. Now that we know that which letter X, Y, or Z would correspond to the mean, median, and mode. Well, recall, recall that in that in a right skewed distribution. Now rightscu distribution. Then the general order is that the mode is less than the median and the median is less than the mean. And here we have our three values here X, Y, and Z. So let's try to match this pattern to X, Y, and Z because no, this would mean then that here X or least value two days would represent the mode, OK. And that makes sense because the tallest bar is, let's just write that here, the tallest bar is at 2 vacation days, OK? And with the highest frequency of 10 employees, that means the mode is 2. So that's what we know for sure that X is the mode. Next, based on the order, this would imply that Y is the median. Now Y represents 3 days, and the median is the middle value in the order data. Since the data is right skewed and 3 is between the mode and the mean, it's likely then that Y is the median. Finally, by that order that must be in Z4 days represents the mean. I know that makes sense because the mean is pulled toward the tail in a rights distribution. So that means it will lie to the right of the median. Therefore, the data is right skewed, where X is the mode, Y is the median, and the Z is the mean. Thanks a lot for watching everyone. I hope this video helped.

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