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| Section | Objectives |
|---|---|
| Probability Distributions | - Discrete distributions
|
| Descriptive Statistics | - Data summarization
|
| Regression and Correlation | - Relationship analysis
|
| Probability | - Probability rules
|
| Statistical Inference | - Hypothesis testing
|
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NEW QUESTION # 42
Histogram is best for:
Answer: D
Explanation:
A histogram is used to display the frequency distribution of quantitative numerical data, especially continuous data grouped into intervals or bins. For example, a histogram can show the distribution of heights, test scores, commute times, or weights. Each bar represents a numerical interval, and the height of the bar represents how many observations fall within that interval. Unlike a bar chart, the bars in a histogram usually touch because the intervals form a continuous numerical scale. Option B is incorrect because categorical data are better displayed with a bar chart or pie chart. Option C is incorrect because a scatterplot displays the relationship between two quantitative variables, not the frequency distribution of one variable. Option D is incorrect because a boxplot summarizes median, quartiles, spread, and outliers rather than showing detailed frequency counts. The correct graph for continuous numerical frequency is a histogram. Study Guide references/topics:
histograms, quantitative data, frequency distributions, graphical displays.
NEW QUESTION # 43
A dataset: 2, 4, 6, 8, 10. Variance = ?
Answer: B
Explanation:
Variance measures the average squared distance of data values from the mean. For the dataset 2, 4, 6, 8, 10, the mean is (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. The deviations from the mean are #4, #2, 0, 2, and 4.
Squaring these deviations gives 16, 4, 0, 4, and 16. The sum of squared deviations is 40. Using the sample variance formula, divide by n # 1, where n = 5. Thus, sample variance = 40 ÷ 4 = 10. Option A is correct.
Option C, 6.25, does not result from the standard sample variance computation for these values. The important distinction is whether a problem is using sample variance or population variance; the provided answer set and calculation use the sample variance formula. Study Guide references/topics: variance, mean, squared deviations, sample variance.
NEW QUESTION # 44
Probability of rolling 1, 2, or 3 on die = ?
Answer: D
Explanation:
A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The event "rolling 1, 2, or 3" has three favorable outcomes: 1, 2, and 3. The probability is therefore favorable outcomes divided by total outcomes: 3/6. This fraction simplifies to 1/2. Option B, 1/3, would correspond to two favorable outcomes out of six. Option C, 1/6, is the probability of rolling one specific number only. Option D, 2/3, would require four favorable outcomes out of six. Since exactly half of the die faces are 1, 2, or 3, the correct probability is one- half. This is a direct application of theoretical probability with equally likely outcomes. Study Guide references/topics: die probability, favorable outcomes, sample space, theoretical probability.
NEW QUESTION # 45
Sample mean = 40, SD = 8, n = 16. Standard error = ?
Answer: C
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.
NEW QUESTION # 46
Standard deviation measures:
Answer: D
Explanation:
Standard deviation measures how spread out data values are around the mean. A smaller standard deviation indicates that values are clustered closely near the mean, while a larger standard deviation indicates greater variability. Standard deviation is based on deviations from the mean, squared deviations, variance, and then the square root of variance. It is expressed in the original units of measurement, making it easier to interpret than variance. Option B is incorrect because central tendency is measured by statistics such as the mean, median, and mode. Option C is incorrect because probability measures likelihood, not data dispersion. Option D refers to frequency or the number of observations, not their variability. For example, two classes could have the same mean test score but different standard deviations; the class with the larger standard deviation has more varied scores. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.
NEW QUESTION # 47
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