Which of the following data types is most suitable for storing the number of children in a family?
Explanation:
Discrete data represents countable values, and you can't have a fraction of a child.
The mean of a dataset is 15 and the standard deviation is 3. What percentage of data points lie within 12 and 18?
Explanation:
This refers to the empirical rule (or 68-95-99.7 rule) in statistics. About 68% of the data points in a normal distribution fall within one standard deviation of the mean.
If you toss a coin three times, what is the probability of getting at least one head?
Explanation:
It's easier to calculate the probability of getting NO heads (TTT), which is 1/2 * 1/2 * 1/2 = 1/8. The probability of getting at least one head is the complement: 1 - (1/8) = 7/8.
Which data type is represented by the ranking of athletes in a competition (1st, 2nd, 3rd, etc.)?
Explanation:
Rankings provide order (1st is better than 2nd), but the difference between ranks is not necessarily equal or meaningful in a numerical sense.
What is the mode of the following dataset: 2, 5, 3, 2, 8, 2, 6?
Explanation:
The mode is the value that appears most frequently in a dataset. In this case, the number 2 appears three times, which is more than any other value.
What is the range of the following dataset: 7, 12, 4, 9, 15, 11?
Explanation:
The range is the difference between the highest and lowest values in a dataset. In this case, 15 (highest) - 4 (lowest) = 11.
Which of the following chart types is MOST effective for displaying data that changes over time?
Explanation:
While not explicitly mentioned in the initial list, line graphs are the most effective for showing trends over time. They connect data points with lines, clearly illustrating changes in data over a continuous interval.
A study finds that there is a correlation between ice cream sales and crime rates. What can we conclude from this finding alone?
Explanation:
Correlation does not equal causation. This finding suggests a link between the two variables, but further investigation is needed to understand the nature of the relationship. There could be other factors at play.
In a probability distribution, what does a higher peak indicate?
Explanation:
In a probability distribution, the height of the curve at a particular point corresponds to the probability of that value occurring. A higher peak indicates a greater concentration of probability around that value.
If you want to visualize the proportion of different departments' expenses in a company, which chart type is most appropriate?
Explanation:
Pie charts excel at representing proportions and percentages. Each slice can represent a department, and its size would correspond to the proportion of the total expenses attributed to that department.
What is the probability of getting heads and then tails when flipping a fair coin twice?
Explanation:
Each flip is independent. The probability of heads is 1/2, and the probability of tails is 1/2. So, (1/2)*(1/2) = 1/4.
A researcher wants to survey a sample of students from a university. They randomly select 5 departments and then survey every student within those departments. What sampling method is being used?
Explanation:
Cluster sampling involves dividing the population into clusters (departments in this case) and randomly selecting entire clusters to be surveyed.
Which of the following is an example of a qualitative variable?
Explanation:
Qualitative variables represent categories or attributes. Favorite color is categorical, while the others are numerical.
Events A and B are independent. The probability of A is 0.4, and the probability of B is 0.5. What is the probability of both A and B happening?
Explanation:
For independent events, you multiply the probabilities: 0.4 * 0.5 = 0.2
What is the primary goal of hypothesis testing in statistics?
Explanation:
Hypothesis testing aims to assess the evidence provided by the data against the null hypothesis. It helps us decide whether the observed data is likely or unlikely if the null hypothesis were true.