Final answer:
To make a histogram for the provided IQ test scores, you would choose appropriate bins, count the frequency of scores in each bin, and plot bars accordingly. The average IQ is 100, with scores within one standard deviation (85 to 115) considered average. The histogram may show outliers or skewness if a significant number of scores fall outside the average range.
Step-by-step explanation:
In addressing a student's question about creating a histogram of IQ test scores for 31 seventh-grade girls, it's important to explain what a histogram represents and how it is used to visualize the distribution of a dataset like IQ scores. Since I can't upload an image in this response, I'll provide guidance instead. To make a histogram, you would first need to choose appropriate bins (ranges of IQ scores) that will allow you to group the scores in intervals. You would then count the number of scores that fall into each bin and represent this frequency with bars, thus creating a visual representation of the distribution.
The description of IQ scores provided indicates that the average IQ is 100 with a standard deviation of 15. Scores within one standard deviation (85 to 115) are considered average. The histogram would likely show this distribution with most scores falling within this range. However, the presence of IQ test scores as low as 72 and as high as 132 could indicate outliers or skewness in the plot. For example, if there were a significant number of scores below 85 or above 115, this could suggest a left or right skew respectively.
If we were to discuss the probability of a sample mean for random adults' IQ scores, we would use the normal distribution properties of IQ scores. Knowing the average IQ score (105), the standard deviation (20), and the desired range (85 to 125), we could calculate the probability using standard normal distribution tables or a statistical software. However, this is unrelated to plotting a histogram for the provided dataset of children scores.