# QTR 1 DATE ASSIGNED: Tuesday, October 7Th

INT MATH NAME ______

QTR 1 DATE ASSIGNED: Tuesday, October 7th

PATTERNS IN DATA DUE DATE: Monday, October 13th

WS 6 HOUR ____

1. The table below gives the percentile ranks of SAT mathematics scores for national college-bound seniors from 1995. The highest possible score is 800 and the lowest possible score is 200. Only scores that are multiples of 50 are shown in the table, but other scores are possible.

SAT Math Score / Percentile / SAT Math Score / Percentile / SAT Math Score / Percentile
750 / 99 / 550 / 70 / 350 / 16
700 / 96 / 500 / 57 / 300 / 6
650 / 90 / 450 / 42 / 250 / 1
600 / 82 / 400 / 28 / 200 / 0

a. What percentage of students get a score lower than 650 on the mathematics part of the SAT?

b. What is the lowest score you could get on the mathematics part of the SAT and still be in the top 30% of those who take the test?

c. Estimate what score you would have to get to be in the top half of the students who take this test.

d. Estimate the 25th and 75th percentiles and the interquartile range. In a sentence or two, explain what this interquartile range means.

e. What do you think is the range of scores on an SAT test for a given year?

2. Consider the box plot at the right.

a. What do you suppose the “n = 20” on the plot means?

b. How many values are between 45 and 80?

Between 80 and 100? Greater than 80?

c. Is it possible for the box plot to represent the data below? Explain your reasoning.

50, 60, 60, 75, 80, 80, 82, 83, 85, 90, 90, 91, 91, 94, 95, 95, 98, 100, 106, 110

3. The following table indicates the percentage of the population in each state who speaks a language other than English at home circa 1994. Only people aged five years and older were included.

State / % Who Speak Other Languages / State / % Who Speak Other Languages / State / % Who Speak Other Languages
Alaska / 12.1 / Kentucky / 2.5 / North Dakota / 7.9
Alabama / 2.9 / Louisiana / 10.1 / Ohio / 5.4
Arkansas / 2.8 / Massachusetts / 15.2 / Oklahoma / 5.0
Arizona / 20.8 / Maryland / 8.9 / Oregon / 7.3
California / 31.5 / Maine / 9.2 / Pennsylvania / 7.3
Colorado / 10.5 / Michigan / 6.6 / Rhode Island / 17.0
Connecticut / 15.2 / Minnesota / 5.6 / South Carolina / 3.5
DC / 12.5 / Missouri / 3.8 / South Dakota / 6.5
Delaware / 6.9 / Mississippi / 2.8 / Tennessee / 2.9
Florida / 17.3 / Montana / 5.0 / Texas / 25.4
Georgia / 4.8 / Nebraska / 4.8 / Utah / 7.8
Hawaii / 24.8 / New Hampshire / 8.7 / Virginia / 7.3
Iowa / 3.9 / New Jersey / 19.5 / Vermont / 5.8
Idaho / 6.4 / New Mexico / 35.5 / Washington / 9.0
Illinois / 14.2 / Nevada / 13.0 / Wisconsin / 5.8
Indiana / 4.8 / New York / 23.3 / West Virginia / 2.6
Kansas / 5.7 / North Carolina / 3.9 / Wyoming / 5.7

a. Make a box plot of the data for the states that are on the edge of the U.S. That includes Alaska, Hawaii, and any state that touches an ocean, Canada, or Mexico. (They are bolded in the table). Then create a box plot of the remaining interior states below the border box plot.

b. Describe the differences between the two box plots. Why do you think there are these differences?

4. The box plots below represent the amounts of money (in dollars) carried by all of the people surveyed in four different places at a mall.

a. Which group of people has the smallest range in the

amounts of money? The largest?

b. Which group of people has the smallest IQR in the

amounts of money? The largest?

c. Which group of people has the largest median amount of money?

d. Which group of people has the most symmetrical distribution?

e. Which group of people do you think might be high school students standing in line for tickets at a movie theater on Saturday night? Explain your reasoning.