Problem Solving and Data Analysis Flashcards

A scatter plot shows hours studied (x) vs. test score (y). The line of best fit is y = 8x + 42. What score does the model predict for 5 hours of study?

Answer: 82

y = 8(5) + 42 = 40 + 42 = 82.

In a class of 30 students, 18 passed math, 20 passed English, and 12 passed both. How many students passed neither subject?

Answer: 4

By inclusion-exclusion: passed at least one = 18+20-12 = 26. Passed neither = 30-26 = 4.

The table below shows monthly sales data. What is the mean monthly sales? Month: Jan, Feb, Mar, Apr, May Sales: $3,200, $4,800, $2,600, $5,400, $4,000

Answer: $4,000

Mean = (3200+4800+2600+5400+4000)/5 = 20000/5 = $4,000.

A survey of 200 people found that 35% prefer coffee and 45% prefer tea. The rest prefer neither. How many people prefer neither?

Answer: 40

35% + 45% = 80% prefer coffee or tea. 20% prefer neither. 0.20 × 200 = 40.

A data set has values: 12, 15, 11, 18, 14, 13, 20, 9, 16, 12. What is the median?

Answer: 13.5

Sorted: 9,11,12,12,13,14,15,16,18,20. Median = average of 5th and 6th: (13+14)/2 = 13.5.

If a bag contains 4 red, 6 blue, and 2 green marbles, what is the probability of randomly selecting a blue marble?

Answer: 1/2

Total marbles = 12. Blue marbles = 6. P(blue) = 6/12 = 1/2.

A two-way table shows that 60 students play sports, of whom 25 also play music. Of 40 students who don't play sports, 15 play music. What percentage of all students play music?

Answer: 40%

Total students = 100. Music players = 25+15 = 40. Percentage = 40/100 = 40%.

A company's profits grew from $50,000 in Year 1 to $80,000 in Year 4. What is the average annual increase?

Answer: $10,000

Total increase = $30,000 over 3 years (from year 1 to year 4). Average = $30,000/3 = $10,000/year.