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.

1. how would you describe the shape of the distribution of mathematics test scores? please explain.

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

Explanation:

Step1: Analyze the histogram

The histogram shows that the data is concentrated around the middle - scores (around 60 - 75), with tails on both the lower and higher ends.

Step2: Compare mean and median

The mean is 66.5 and the median is 67. Since the mean and median are close, the distribution is approximately symmetric. Also, the box - plot shows that the median is in the middle of the box and the whiskers are relatively equal in length on both sides.

Answer:

The distribution of mathematics test scores is approximately symmetric. The mean (66.5) and median (67) are close, and the histogram shows a roughly equal spread of data on either side of the center, and the box - plot has a median near the center of the box with relatively equal whisker lengths.