Question

Here are the summary statistics for Verbal SAT scores for a high school graduating class:a)Create side-by-side boxplots comparing the scores of boys and girls as best you can from the information given.b)Write a brief report on these results. Be sure to discuss the shape, center, and spread of the scores.

Answer 1

Explanation:

In a box and whisker plot:

• Ends of the box are the upper and lower quartiles, so the box spans the interquartile range
• Median is marked by a line inside the box
• Whiskers are the two lines outside the box that extend to the highest and lowest observations.  

(please refer to the diagram below)

Example:

Macy works at a store. She recorded her sales for the past 11 months:

51, 27, 25, 22, 63, 44, 38 , 41, 20, 6, 43.

We arrange them in ascending order:

6, 20, 22, 25, 27, 38, 41, 43, 44, 51, 63.  

Calculate the median and quartiles:

$Q_1 = (\frac{1}{4})(n+1)^{th} \ value\\\\Q_2 = (\frac{2}{4})(n+1)^{th} \ value\\\\Q_3 = (\frac{3}{4})(n+1)^{th} \ value$

$Q_1 = (\frac{1}{4}) \times 12 = 3^{rd} \ value \rightarrow 22\\\\Q_2 = (\frac{2}{4}) \times 12 = 6^{th} \ value \rightarrow 38\\\\Q_3 = (\frac{3}{4}) \times 12 = 9^{th} \ value \rightarrow 44$

Minimum value: 6

Maximum value: 63