3. The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey obtained in the data hsb2 in the package openintro (a) Draw boxplots for the distribution of reading and writing scores. (b) Draw a histogram of the difference between reading and writing scores. (c) Based on a visual inspection of these plots is there a clear difference in the average reading and writing scores

Answer / Explanation:

To properly answer this question, let us first understand what a box plot is and an histogram.

A box plot is the standard method for showcasing the distribution of data based on a five number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”). It should also be noted that a vertical line usually goes through the box plot at the median.

While

Histogram is the graphical representation of data using bars of different altitude. In a histogram, each rectangular bars are grouped into ranges. Taller rectangular bars show more of values or data falls in that range. A histogram displays the shape and spread of continuous sample data.

On defining and understanding the aforementioned principles, if we go ahead to answer the question, we have:

(a) Draw box plots for the distribution of reading and writing scores

The diagram can be found below.

(b) Draw a histogram of the difference between reading and writing scores

The requested diagram has been attached and can be found blow.

(c) Based on a visual inspection of these plots is there a clear difference in the average reading and writing scores

Yes: The means seem slightly different, but the distribution of differences looks quite normal. However, The scores of either reading or writing are independent, but one student is likely to have scores for both sides in the sample.

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