Learn About Misleading Statistics

TenMarks teaches you how to understand misleading statistics.

Learn About Misleading Statistics In this lesson, let’s learn about misleading statistics, okay. I'm going to use a couple of examples to show you how certain statistics can often be misleading. So in this table, ABC Corporation claims that the average salary of its employees is more than 60,000. All the average salary in XYZ is only 25,000. Use the table to explain there 0030, okay. So let’s look at how they got to it. So for ABC Corp, what is the mean? The mean is well it tells us how many employees they have is the sum of all the salary. So we have 500,000 which is one person plus 400,000 which is another person plus 240,000 which is the third person is only one of each plus 5 times 20,000 plus eight times fifteen thousand plus seven times nine thousand, right. Let’s do a total this. So that’s 500,000+400,000+240,000+5×20,000 is 100,000+8×15,000 is 120,000+7×9 is 63,000, okay. So what is the mean? The mean of this total one is 1,423,000 divided by 23 which is about $60,000 approximately. It’s actually $61,869.00, right. Now for ABC, the mean is this. Let’s calculate the median, okay for ABC. What is the median salary? This would be the salary between the 11th and 12th employee, right. 11th and 12th employee in this case would be seven employees to the bottom out right here, so 11th employee, 12th employee would be 15,000, okay that would be the median. Now let’s try and do the mean of XYZ. So for XYZ, the mean if we total it up would be the sum of all these, exactly what we did divided by 23 would get you the mean of B approximately 36,000. And the median will be the 11th and 12th employee, right. So in this case 11th and 12th employee would be 25,000. So what they are trying to do is basically show you that they view the mean to describe their own salary and the median to describe the salary of the other company. They haven’t used the fair comparison, okay. So which one should you be working at if you can work as a president, the first vice-president, or the second vice-president then this is a better place to work, right. This is a better place to work. But if you're not going to be one of this, then you're much better off working here because the salaries are going to be much higher compared to this place. So even though the statistics tell us the average salary of both companies, it’s actually misleading. Let’s try something different. Let’s look at the second value which is the line plot shows Mike’s test scores which measure might be use to emphasize the high scores. So for example, let’s look at the mean. The mean in this case is 80×1, right. this is 80+83+84+84+86+88+90+90+92+94+96+96+96, I add all the individual values, right and divided by the total number 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ,13, 14, 15 which if I add and divide gives me the mean is 88.66. The median is the middle value. 1, 2, 3, 4, 5, 6, 7, 8 value is the median, right, out 15. So the median is 90 and mode is the one which has the highest frequency. That’s this one, 96. So if I want to highlight the highest scores, I would use the mode because that shows me the highest scores among these three.