The companion set to Workshop 8. Twelve real SAT-style questions on percents and unit conversions, tables and charts, and center and spread. Three moves: scale it, read it, describe it.
Data questions are careful reading plus a little arithmetic. Before you calculate, name your first move. Scale it: find the base of the percent, multiply percent changes as factors, and stack unit conversions until only the units you want are left. Read it: follow the labels to the one number you need, and read the axis step, not the bar's height by eye. Describe it: is the question about the center (mean, median) or the spread (range, standard deviation)? Here is how the wrong answers try to trip you:
Wrong Whole. Divides by the wrong total: the whole table instead of the group the question names, or the part instead of the whole.
Added, Not Multiplied. Adds or subtracts back-to-back percent changes instead of multiplying the factors.
Flipped Factor. Turns a conversion factor upside down, or forgets to square it for area units.
Misread Scale. Counts gridlines as if each step were 1 (or 10) instead of reading the axis step.
Wrong Bar / Wrong Cell. Reads the right kind of number from the wrong bar, row, or column.
Median Moved. Assumes an extreme value drags the median, or takes the middle bar without sorting first.
Question 1 of 12
Scale ItMedium
A team played $50$ games and won $18$ of them.
What percentage of its games did the team win?
The takeaway: Divide games won by games played: $\frac{18}{50} = 0.36$, and $0.36 \times 100 = 36$, so the team won $36\%$ of its games.
Read ItMedium
The bar chart shows the number of students enrolled in each of four language classes at a school.
How many students are enrolled in the Mandarin class?
The takeaway: Find the Mandarin bar and read its height against the scale, noting that each gridline step represents 6 students. The bar tops out at the gridline for 42, so 42 students are enrolled in Mandarin.
Describe ItMedium
A data set is shown.
61, 58, 74, 66, 58, 80
What is the range of the data set?
The takeaway: The range is the largest value minus the smallest value: $80 - 58 = 22$.
Scale ItChallenge
The number of members in a hiking club increased by $40\%$ during its second year and decreased by $30\%$ during its third year.
Which of the following describes the net change in membership from the start of the second year to the end of the third year?
The takeaway: The net multiplier is $1.40 \times 0.70 = 0.98$. Since $0.98$ is $2\%$ below $1$, the membership decreased by $2\%$ overall.
Read ItMedium
The bar chart shows the total rainfall, in millimeters, recorded in a city during each of four months.
How many more millimeters of rain fell in April than in June?
The takeaway: Read the April bar and the June bar from the chart. April's bar reaches 120 millimeters and June's bar reaches 100 millimeters, so the difference is 120 minus 100, which is 20 millimeters.
Describe ItChallenge
The bar graph shows the number of bicycles a shop rented out on each of five days.
What was the median number of bicycles rented per day for the five days shown?
The takeaway: The bar heights are 36, 48, 24, 40, and 56. Ordering them gives 24, 36, 40, 48, 56, and the middle value of the ordered list is 40, so the median is 40.
Scale ItMedium
A satellite passes over a constant 240 kilometers of ground track every 30 seconds.
What is its ground speed, in meters per second? $(1\text{ kilometer} = 1{,}000\text{ meters})$
The takeaway: Stack the conversion so the units cancel: $\dfrac{240 \text{ km}}{30 \text{ s}} \times \dfrac{1{,}000 \text{ m}}{1 \text{ km}} = 8{,}000$ meters per second. Kilometers sit once on top and once on the bottom, so they cancel and leave meters per second.
Read ItMedium
The table shows the number of pastries sold at a bakery in one morning.
Pastry
Sold
Muffin
10
Croissant
12
Bagel
14
Scone
14
Total
50
What percent of the pastries sold were croissants?
The takeaway: There were $12$ croissants out of $50$ total, so $12/50 \times 100 = 24$ percent.
Describe ItChallenge
A data set is shown.
12, 15, 18, 21, 24
The value 24 is replaced with the value 60. Which statement correctly describes how the mean and the median of the data set are affected?
The takeaway: The original data set has mean $(12 + 15 + 18 + 21 + 24)/5 = 90/5 = 18$ and median 18 (the middle value). After the replacement, the data set is 12, 15, 18, 21, 60. The middle value is still 18, so the median is unchanged. The mean becomes $(12 + 15 + 18 + 21 + 60)/5 = 126/5 = 25.2$, an increase. The mean uses every value, so swapping 24 for the much larger 60 raises it, while the median depends only on the middle position, which did not move.
Scale ItChallenge
A tile installer covers a floor with tiles that cost a constant 90 dollars per square yard.
At this rate, what is the cost, in dollars per square foot? $(1\text{ yard} = 3\text{ feet})$
The takeaway: Square the conversion factor for area units: $\dfrac{90 \text{ dollars}}{1 \text{ yd}^2} \times \left(\dfrac{1 \text{ yd}}{3 \text{ ft}}\right)^2 = \dfrac{90}{9} = 10$ dollars per square foot. A square yard is $3^2 = 9$ square feet.
Read ItChallenge
The table classifies 120 survey respondents by region and by whether they prefer coffee or tea.
Region
Coffee
Tea
Total
North
30
18
48
South
44
28
72
Total
74
46
120
Given that a respondent lives in the North region, what is the probability that the respondent prefers tea?
The takeaway: The condition 'North region' restricts to the 48 North respondents. Of those, 18 prefer tea, so $P=\frac{18}{48}=0.375$.
Describe ItChallenge
Data set A consists of the values 12, 15, 18, 21, and 24. Data set B consists of the values 12, 13, 18, 23, and 24.
Which of the following statements correctly compares the two data sets?
The takeaway: Both data sets have a sum of 90, so both means are 18, and both medians are 18. Both ranges are $24 - 12 = 12$. But data set B's values cluster farther from 18 on average (13 and 23 are farther from the mean than 15 and 21), so B has the greater standard deviation.
0 / 12
Data questions are careful reading plus a little arithmetic, and a tutor who watches you work shows you which move to make first. Book a free 30-minute consultation and we'll map out a plan to reach your SAT goal.
Book your free consultation to discuss your student's test, timeline, and prep options.
First Tutoring Hour FreeTop 5% of Tutor Applicants
Our best students have gained 300+ SAT points; most who complete our program gain 150 to 300.
Individual results vary with starting score, effort, and time invested.
★★★★★
“We've been very impressed with the methodical, detailed tutoring by Ingo. He's been working with our son on his SAT and ACT prep. Extremely pleased so far!”
We have your information and a member of our team will reach out to schedule your consultation. If you'd like to talk sooner, call us at (801) 508-4080.
