IQ scores distribution of IQ scores is 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?
See earlier Q & A.
To find the area under the curve, you need to calculate the probability of a specific range of IQ scores. In this case, since the IQ scores follow a normal distribution, you can use the z-score formula.
Z-score = (X - mean) / standard deviation
1. Area under the curve:
The area under the curve represents the probability of a specific range of IQ scores. To find the area under the entire curve, you would need to find the probability from negative infinity to positive infinity, which is equal to 1.
2. Median:
The median is the middle value of a distribution. In a normal distribution, the median is equal to the mean. In this case, the median would be 100.
3. Mode:
The mode is the most frequently occurring value in a distribution. In a normal distribution, the mode also corresponds to the mean. Therefore, the mode would be 100 as well.
Please note that the mode is not always informative about the distribution when dealing with continuous variables like IQ scores, as the probabilities for each value are infinitesimally small. The mean and median are more commonly used to describe central tendency in a normal distribution.