IQ scores distribution of IQ scores is not normally distributed
standard with a mean of 100 and a standard deviation of 15, which is represented by a bell-shaped graphical.
What is the area under the curve?
What is the median?
What is the mode?
Since you say "distribution of IQ scores is NOT normally distributed," bell-shaped graphical does not represent it. Therefore, cannot make estimates. If it was normal, mean = mode = median.
To find the area under the curve, median, and mode, we need to refer to the normal distribution. While you state that the distribution of IQ scores is not normally distributed, for the purpose of answering these questions, we will assume a normal distribution.
1. Area under the curve:
To find the area under the normal curve, we need to specify a range or a probability. Without a specific range or probability, we cannot provide an exact answer. However, we can calculate the area under the curve within a certain number of standard deviations from the mean. Based on the empirical rule, approximately 68% of the data falls within one standard deviation, around 95% falls within two standard deviations, and nearly 99.7% falls within three standard deviations. These percentages can provide a rough estimate of the area under the normal curve.
2. Median:
In a normal distribution, the median coincides with the mean, which is given as 100 in this case. Therefore, the median of this distribution is 100.
3. Mode:
In a normal distribution, the mode refers to the most frequent value or values. Since a normal distribution can have multiple modes (if the distribution has multiple peaks or dips), we need more information or a specific dataset to determine the mode of IQ scores.
In summary:
1. The area under the curve depends on the specified range or probability.
2. The median is equal to the mean, which is 100 in this case.
3. The mode requires more information or a specific dataset for determination.