Question

part 1: describing a sample of quantitative data
a large sample of high school students complete a mathematics test that is worth 100 points. the graphs and table of summary statistics given below are meant to help us better understand this distribution of data. please use this information to answer questions 1 through 12.

mean standard deviation minimum q1 median q3 maximum
66.5 14.9 19 57 67 77 100

1 how would you describe the shape of the distribution of mathematics test scores? please explain.
i would describe the shape of the distribution as slightly symmetric and maybe slightly skewed left because the mean and the median are close in proximity of each other and histogram shows a pretty equal variation from each side of the graph. i would say that the graph isnt fully symmetric but not fully skewed either.
2 we dont tell you the size the sample, but sample size is something you should be able to estimate based on what you see in one of the graphical displays above. tell us how many students you think are in this sample and how you arrived at your estimate.

Explanation:

Step1: Analyze histogram shape

The histogram has a peak near the middle and tapers off on both sides. The mean (66.5) and median (67) are close, which is a characteristic of a symmetric - like distribution. Also, the spread on both sides of the peak in the histogram seems somewhat similar.

Step2: Consider skewness

Since the mean is slightly less than the median, it indicates a slight left - skewness. But overall, the distribution is close to symmetric.

Answer:

The distribution of mathematics test scores is slightly symmetric with a slight left - skew. This is because the mean and median are close in value and the histogram shows a relatively equal spread on both sides of the peak with a slight pull to the left as the mean is less than the median.