Normal score
A normal score, also known as a Z-score, is a way of deciding how far away a particular number is from the average of all the numbers in a particular group or set. For example, if you were to take a test and got a score of 80 out of 100, that might seem really good to you at first. But if you found out that the average score for everyone who took the test was 90 out of 100, suddenly your score doesn't seem as good anymore!
A normal score helps us figure this out by taking into account the average (also called the mean) and the standard deviation of a set of numbers. The standard deviation is a measure of how spread out the numbers are in the set. For example, if 90% of people who took the test got a score between 70 and 95, the standard deviation might be around 12 (meaning that most scores are within 12 points of the average).
To find your normal score, you take your own score and subtract the average, then divide by the standard deviation. This tells you how many standard deviations away from the average you are. If your normal score is 0, that means you got exactly the average score. If your normal score is -1, that means your score was one standard deviation below the average. If your normal score is +2, that means your score was two standard deviations above the average.
Normal scores are useful because they allow us to compare scores from different groups or sets that might have different averages and standard deviations. For example, if you want to compare test scores from students in different schools, you could use normal scores to account for differences in the difficulty of the tests or the quality of the teaching. Overall, normal scores help us understand how well we're doing compared to other people or groups, and give us a way to measure our own progress over time.
A normal score helps us figure this out by taking into account the average (also called the mean) and the standard deviation of a set of numbers. The standard deviation is a measure of how spread out the numbers are in the set. For example, if 90% of people who took the test got a score between 70 and 95, the standard deviation might be around 12 (meaning that most scores are within 12 points of the average).
To find your normal score, you take your own score and subtract the average, then divide by the standard deviation. This tells you how many standard deviations away from the average you are. If your normal score is 0, that means you got exactly the average score. If your normal score is -1, that means your score was one standard deviation below the average. If your normal score is +2, that means your score was two standard deviations above the average.
Normal scores are useful because they allow us to compare scores from different groups or sets that might have different averages and standard deviations. For example, if you want to compare test scores from students in different schools, you could use normal scores to account for differences in the difficulty of the tests or the quality of the teaching. Overall, normal scores help us understand how well we're doing compared to other people or groups, and give us a way to measure our own progress over time.
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