Problem Solving & Data Interpretation Flashcards

A linear model for quantity sold (y) based on price (x) is y = −3x + 90. What quantity is predicted when the price is 20?

Answer: 30

y = −3(20) + 90 = −60 + 90 = 30.

Two data sets have the same mean of 50. Set A has a standard deviation of 5 and Set B has a standard deviation of 15. Which statement is true?

Answer: Set B's data is more spread out than Set A's

Standard deviation measures spread; a higher standard deviation means the data is more spread out from the mean.

A table shows: 10 hours worked = $80 earned, 20 hours = $160, 30 hours = $240. What is the hourly pay rate?

Answer: $8/hr

Dividing earnings by hours for any row: $80 ÷ 10 = $8 per hour.

A savings account earns 5% annual interest compounded annually. If $1,000 is deposited, what is the balance after 2 years?

Answer: $1,102.50

After year 1: $1,000 × 1.05 = $1,050; after year 2: $1,050 × 1.05 = $1,102.50.

A graph shows a straight line passing through (0, 0) and (4, 120), where the x-axis is time in hours and the y-axis is distance in miles. What does the slope represent?

Answer: The speed in miles per hour

Slope = rise/run = 120 miles / 4 hours = 30 mph, which represents speed.

A researcher tests whether a new study method improves test scores. One group uses the new method and another uses traditional methods for the same subject. Which variable must be controlled to ensure a valid comparison?

Answer: The amount of study time per session

Study time must be equal between groups so that any score difference is attributable to the method, not the amount of time spent.

A histogram shows a right-skewed distribution of household incomes in a neighborhood. Which measure of center best represents the typical household income?

Answer: Median, because it is resistant to extremely high values

In a right-skewed distribution, the mean is pulled up by high outliers, so the median is a more representative measure of the center.