BMST - Basic Math and Science Data Interpretation and Probability Questions and Answers 2 — Questions and Answers

Question 1: A dataset has values: 4, 7, 7, 9, 13. What is the median?

7 (Correct answer)
8
9
4

Correct answer: 7

The data is already sorted. The middle value (3rd of 5) is 7.

The median is the middle value when data is arranged in order. With 5 values (4, 7, 7, 9, 13), the middle position is the 3rd value: 7. For an even number of values, the median is the average of the two middle values. The median is useful because it is not affected by extreme outliers.

Question 2: If you flip a fair coin twice, what is the probability of getting heads both times?

1/4 (Correct answer)
1/2
3/4
1/8

Correct answer: 1/4

P(H and H) = 1/2 × 1/2 = 1/4, since the flips are independent events.

For independent events, multiply their individual probabilities. Each coin flip has P(heads) = 1/2. Since the two flips are independent, P(heads on first AND heads on second) = 1/2 × 1/2 = 1/4. The sample space is {HH, HT, TH, TT}, and only 1 of 4 outcomes is HH, confirming the 1/4 probability.

Question 3: A bar graph shows sales of 200, 350, and 150 for three months. What is the total?

700 (Correct answer)
350
500
600

Correct answer: 700

Sum all values: 200 + 350 + 150 = 700.

Reading data from a bar graph requires identifying the value each bar represents. Here the three bars represent 200, 350, and 150. The total is 200 + 350 + 150 = 700. Bar graphs are effective for comparing quantities across categories and reading approximate values from the height or length of each bar.

Question 4: What is the range of the dataset: 12, 5, 8, 19, 3?

16 (Correct answer)
14
19
3

Correct answer: 16

Range = maximum - minimum = 19 - 3 = 16.

The range is the simplest measure of spread (variability) in a dataset. It is calculated as the difference between the maximum and minimum values. For {3, 5, 8, 12, 19}, the maximum is 19 and the minimum is 3, so the range = 19 - 3 = 16. While easy to compute, the range only uses two data points and is sensitive to outliers.

Question 5: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?

1/2 (Correct answer)
1/3
3/10
2/5

Correct answer: 1/2

Total marbles = 10. P(blue) = 5/10 = 1/2.

Probability = favorable outcomes / total outcomes. There are 3 + 5 + 2 = 10 marbles total, and 5 are blue. P(blue) = 5/10 = 1/2 = 0.5, or 50%. This is a simple probability calculation assuming each marble is equally likely to be drawn.

Question 6: The mean of five test scores is 82. If four scores are 78, 85, 90, and 75, what is the fifth score?

82 (Correct answer)
80
84
86

Correct answer: 82

Total = 82 × 5 = 410. Sum of four = 328. Fifth score = 410 - 328 = 82.

Since mean = sum of all values / number of values, and the mean is 82 with 5 scores, the total sum must be 82 × 5 = 410. The sum of the four known scores is 78 + 85 + 90 + 75 = 328. Therefore, the fifth score = 410 - 328 = 82. This reverse calculation is a common application of the mean formula.

BMST - Basic Math and Science Data Interpretation and Probability Questions and Answers 2

A dataset has values: 4, 7, 7, 9, 13.
What is the median?