Statistics and Data Analysis Terms
Focus not only on the terms for the statistics and analyses you’ll calculate but also on their interpretation, especially in the context of a statistics problem. Answer the following problems about different statistics and data analysis terms.
Which of the following data sets has a median of 3?
(A) 3, 3, 3, 3, 3
(B) 2, 5, 3, 1, 1
(C) 1, 2, 3, 4, 5
(D) 1, 2, 4, 4, 4
(E) Choices (A) and (C)
Answer: E. Choices (A) and (C) (3, 3, 3, 3, 3; 1, 2, 3, 4, 5)
To find the median, put the data in order from lowest to highest, and find the value in the middle. It doesn’t matter how many times a number is repeated. In this case, the data sets 3, 3, 3, 3, 3 and 1, 2, 3, 4, 5 each have a median of 3.
Susan scores at the 90th percentile on a math exam. What does this mean?
Answer: It means that 90% of students who took the exam had scores less than or equal to Susan’s.
A percentile shows the relative standing of a score in a population by identifying the percent of values below that score. Susan scored in the 90th percentile, so 90% of the students’ scores are less than or equal to Susan’s.
Suppose that the results of an exam tell you your z-score is 0.70. What does this tell you about how well you did on the exam?
Answer: Your score is 0.70 standard deviations above the mean.
A z-score tells you how many standard deviations a data value is below or above the mean. If your z-score is 0.70, your exam score is 0.70 standard deviations above the mean. It doesn’t tell you your actual score or how many students scored above or below you, but it does tell you where a data value stands, compared to the average exam score.
A national poll reports that 65% of Americans sampled approve of the president, with a margin of error of 6 percentage points. What does this mean?
Answer: It means that it’s likely that between 59% and 71% of all Americans approve of the president.
The margin of error tells you how much your sample results are likely to change from sample to sample. It’s measured as “plus or minus a certain amount.” In this case, the margin of error of 6% tells you that the result from this sample (65% approving of the president) could change by as much as 6% on either side.
Therefore, in using the sample results to draw conclusions about the whole population, the best you can say is, “Based on the data, the percentage of all Americans who approve of the president is likely between 59% (65% – 6%) and 71% (65% + 6%).”
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