HLT 540 Grand Canyon Week 5 Discussion 2

When students talk about “grading on the curve,” how does that apply to the normal distribution?

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The “grading on the curve” and normal distribution

Introduction

Grading on a curve is a common method of assigning grades to students in school. The idea is that you try to grade the same way as everyone else does, so that your student’s grade will fall somewhere between the median and mean of all student grades.

Normal distribution is a statistical term that describes data in which the numbers tend to cluster around the median.

The normal distribution is a statistical term that describes data in which the numbers tend to cluster around the median. It’s also called Gaussian or bell curve, because it looks like a bell when graphed on a graph.

The normal distribution has two basic properties:

• Symmetrical – The density function of every point on this curve is equal to 1/2 (or 50%). So if you have 1000 observations from your data set, then 50% will lie above and below this line at any given time.

• Flat – The area under this curve between any two points is always equal to their distance apart (i.e., it doesn’t matter whether one observation is more than another).

Grading on a curve means that grades are assigned based on how well students perform compared to other students taking the same test.

Grading on a curve means that grades are assigned based on how well students perform compared to other students taking the same test. This is done through a system of curves and grade points. The teacher can adjust the curve by changing its slope and shape, so that it’s easier or harder for students at different ranges of ability.

The most common type of grading curve is called A/B/C—the letters stand for Average (A), Below Average (B), and Outstanding (C). These refer to percentages:

• A represents 100% of all eligible students who receive an “A” or better;

• B represents 50% of all eligible students who receive an “A” or better;

• C represents 25% of all eligible students who receive an “A” or better

The normal distribution curve is S-shaped and symmetrical.

The normal distribution curve is S-shaped and symmetrical. It has a single peak, and it’s finite in both directions.

The peak at the center of this distribution is your median (the middle number), which separates it from other curves that have more outliers on either end (like an exponential or lognormal).

One popular example of normal distribution is height.

One popular example of normal distribution is height. Think about how tall you are, or how short your friends are. Your height is probably not exactly 5 feet 10 inches (or whatever). The mean and median are both equal to 5 feet 10 inches, but the mode can be anywhere between 5 feet 4 inches and 5 feet 11 inches.

In this case, the curve flattens out at both ends: those who have been measured as very short (under 4 foot) will have their numbers on the right side of their interval (measured from left to right) and those who are measured as being very tall will be on the left side of their interval (measured from left to right).

The curve flattens out at both ends, so there are fewer outliers at the very high and low ends.

The curve flattens out at both ends, so there are fewer outliers at the very high and low ends.

For example, if you have an exam that has a 50 percent passing rate and you have 100 students taking it, then 20 students will fail (20 percent). But if you have an exam where only half of those who take it pass (50 percent), then only 10 students will fail (10% instead of 20%). In this second case, we would consider our curve to be S-shaped because there are more failures in one place than another—and this is exactly what we want!

The curve has a single peak; half of the values fall to one side of the central point, and half fall to the other side.

The curve has a single peak; half of the values fall to one side of the central point, and half fall to the other side. There are two types of curves: symmetrical and skewed. The symmetrical case is where both ends are equal in size while the skewed case has one end much larger than the other (e.g., an extreme positive or negative value).

The mean, median and mode all equal values on this type of curve because they’re all related by their respective relationships with each other. This can be seen by looking at how they fit together:

In normal distribution, the mean, median and mode are all equal.

In a normal distribution, the mean, median and mode are all equal. The mean is the middle value of a set of numbers. The median is the middle value when the values are arranged in order. The mode is the most common value in a set of numbers

If data follows normal distribution, they show smooth bell-curve when plotted in a graph.

If data follows normal distribution, they show smooth bell-curve when plotted in a graph.

Normal distribution is a statistical term that describes data in which the numbers tend to cluster around the median.

Understanding normal distributions can help you understand probability and statistics.

Normal distributions are a common way to describe data. A normal distribution is the most common distribution in statistics, and it can be used to describe many phenomena that occur in nature and society.

The graph above displays the normal distribution for three points, with μ=1 and σ=5 (the standard deviation). The horizontal axis represents the mean (average), while the vertical axis represents either positive numbers or negative numbers depending on whether you’re counting up or down from there. If you take one point at random from this plane then it would have a probability of 1/2 that your sample will fall within +/-1 standard deviation from its mean—i.e., 2-sigma errors

Conclusion

Normal distribution is a useful concept to understand if you want to understand statistics, probability and probability theory. If your data follows the normal curve, then it shows smooth bell-curve when plotted in a graph. This means that the data points are evenly distributed around one central point.

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