nothing.
The sum of the differences between each score in a distribution and the mean of those scores is always zero because the mean is defined as the balance point of the distribution. When you subtract the mean from each score, the positive differences (scores above the mean) exactly cancel out the negative differences (scores below the mean). This property ensures that the total deviation from the mean is zero, reinforcing the concept that the mean represents the central tendency of the data.
The differences in test scores, or predictions from those scores, between two or more subgroups of the population that are matched on the underlying construct being measured.
Research has shown that there are persistent differences in IQ test scores across different racial and ethnic groups in the US, with some groups consistently scoring higher or lower on average than others. However, it is important to note that while there may be differences in average scores, individual differences within each group are greater than differences between groups.
3
To find the area under the normal curve between z scores of 1.82 and 2.09, you can use the standard normal distribution table or a calculator. The area corresponding to a z score of 1.82 is approximately 0.9656, and for 2.09, it is about 0.9817. Subtracting these values gives the area between the two z scores: 0.9817 - 0.9656 = 0.0161. Thus, the area under the curve between z scores of 1.82 and 2.09 is approximately 0.0161, or 1.61%.
2
They should be.
Normal IQ scores for children typically fall between 90 and 110. Scores above 130 are considered superior, while scores below 70 are indicative of intellectual disability. It's important to consider other factors when interpreting IQ scores, such as a child's age and individual strengths and weaknesses.
In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean (between -1 and +1 standard deviations). About 95% of scores fall within two standard deviations (between -2 and +2 standard deviations). Therefore, the percentage of scores that falls specifically between the mean and -2 to 2 standard deviations is about 95% minus the 50% that is below the mean, resulting in approximately 45%.
Nope it all depends on the individual
Chicago schools have the lowest test scores.)~:
In a normal distribution, approximately 76.5% of the data falls between z-scores of -1.16 and +1.16. This is calculated using the cumulative distribution function for the standard normal distribution, which gives the area under the curve between these two z-scores. Thus, the area represents the proportion of the data within that range.