Numeracy: Statistics and Probability Flashcards

A bag contains 15 marbles: 6 are red, 5 are blue, and 4 are green. If one marble is drawn at random, what is the probability that it is blue?

Answer: 1/3

Probability is calculated as the number of favourable outcomes divided by the total number of possible outcomes. There are 5 blue marbles (favourable outcomes) and a total of 15 marbles (6+5+4). Therefore, the probability is 5/15, which simplifies to 1/3.

A student's test scores for the semester are: 88, 92, 84, 92, 78. What is the median of these scores?

Answer: 88

The median is the middle value in a data set when the numbers are arranged in order. First, order the scores from lowest to highest: 78, 84, 88, 92, 92. The middle number in this ordered set is 88.

The table below shows the preferred sport for a group of Year 9 and Year 10 students. How many Year 10 students prefer Soccer?

Answer: 18

To find the number of Year 10 students who prefer Soccer, locate the 'Year 10' row and the 'Soccer' column. The value in the cell where this row and column intersect is the answer. In the table, the intersection of the 'Year 10' row and the 'Soccer' column is 18.

A weather forecast predicts a 75% chance of rain on Tuesday, a 1/2 chance of rain on Wednesday, and a 0.8 chance of rain on Thursday. On which day is it most likely to rain?

Answer: Thursday

To compare the likelihoods, convert all probabilities to the same format (e.g., decimals or percentages). Tuesday: 75% = 0.75. Wednesday: 1/2 = 0.50. Thursday: 0.8 = 0.80. The highest value is 0.80, which means Thursday is the most likely day for rain.

The daily maximum temperatures (in degrees Celsius) recorded for one week were: 25, 28, 22, 31, 27, 24, 29. What is the range of these temperatures?

Answer: 9

The range of a data set is the difference between the highest and lowest values. The highest temperature is 31°C and the lowest is 22°C. The range is 31 - 22 = 9.

A scatter plot shows the relationship between the hours students spend studying and their final exam scores. The points on the plot generally trend from the bottom left to the top right. Which of the following is the best interpretation of this plot?

Answer: There is a positive correlation between study hours and exam scores.

When data points on a scatter plot trend upwards from left to right, it indicates a positive correlation. This means that as one variable (study hours) increases, the other variable (exam scores) also tends to increase.