Questions and Answers
If one wanted to calculate summary statistics for salaries at a large company where there are many people with modest salaries and a few with very high salaries, which would be the most appropriate measures of center and spread?
Mr. Jones' class of 32 students had a mean score of 72.4% while Mr. Roberts' class of 29 students had a mean score of 63.4%. What is the mean score of these two classes?
After the times were calculated at a recent cross-country race, it was discovered that the timers started their watches 3 minutes after the gun was shot. If the mean time for the runners was 21.2 minutes and the standard deviation was 2.1 minutes, what would the new measurements be after adjusting the times?
Given the five-number summary: min 12, Q1 17.5, median 24, Q3 30, max 40, what would the upper boundary be (to the nearest hundredth)?
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A set of data was submitted to a calculator and here are the summary statistics: mean = 72.4, std dev = 2.8, median = 66.4. Which is a correct description of this data?
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If you were provided two sets of data, you could compare the two inter-quartile ranges and standard deviations without using a calculator.
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Given the following data output: n = 12, min = 101, Q1 = 102, median = 134, Q3 = 160, max = 270. Which description of the data is best?
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A group of girls on a college campus were polled about their pairs of shoes. If one more girl is polled and submits that she has 12 pairs of shoes, what is the new overall mean for pairs of shoes for all of these girls?
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If a person were to display the below list of data in a stem-plot, which of the following would be used for its setup? 234, 200, 81, 172, 180, 100, 154, 199, 220
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Which of the following could be data that is skewed right? I. Ages of dogs in a kennel II. Heights of adult males at a concert III. Average cost of houses in Florida
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If you are provided the five-number summary of: you can determine that 75% of the data exists between 23 and 30.
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Study Notes
Summary Statistics and Calculations
- Appropriate measures of center and spread for salary data with outliers: median and IQR.
- Mean score combined from two classes: Mr. Jones' (72.4%) and Mr. Roberts' (63.4%) gives an overall mean of 68.1%.
- Adjusted mean time for runners after adding 3 minutes to a mean of 21.2 minutes becomes 24.2 minutes, with standard deviation unchanged at 2.1 minutes.
Data Distribution and Measures
- Five-number summary includes minimum, Q1, median, Q3, and maximum values; for given data, upper boundary is calculated as 48.75.
- Summary statistics indicate that the data is skewed right: mean (72.4), standard deviation (2.8), median (66.4).
- True that inter-quartile ranges and standard deviations of two datasets can be compared without a calculator for given sets.
Data Description and Trends
- Description of dataset with n=12, showing a center at 134 and exhibiting right skewness with at least one outlier identified.
- Average number of pairs of shoes polled: 20 girls average 8 pairs, 10 girls average 15 pairs; new overall average after including a 12-pair response is 10 pairs.
- Setup of stem-plot for data 234, 200, 81, etc. would range the stem from 0 to 23 with leaves from 0 to 9.
Understanding Skewness in Data
- Data potentially skewed right includes the average cost of houses in Florida, indicating a few high-value outliers among a larger dataset.
- The statement regarding the five-number summary indicates falsehood in determining that 75% of the data lies strictly between Q1 (23) and Q3 (30).
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Description
Test your knowledge on summary statistics and measures of center in statistics with this practice test from Chapter 2. Questions focus on different scenarios, including salary calculations and mean scores in classrooms. Perfect for those studying statistics concepts at an introductory level.
