Podcast
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?
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?
- Median and IQR (correct)
- Mean and Standard Deviation
- Mean and IQR
- Mode and Range
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?
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?
- 68.1% (correct)
- 72.4%
- 67.9%
- 63%
- 67.5%
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?
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?
- Mean = 24.2, S = 5.1
- Mean = 24.2, S = 2.1 (correct)
- Mean = 21.2, S = 5.1
- Mean = 21.2, S = 2.1
- Cannot be determined without knowing how many runners there were
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)?
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)?
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?
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?
If you were provided two sets of data, you could compare the two inter-quartile ranges and standard deviations without using a calculator.
If you were provided two sets of data, you could compare the two inter-quartile ranges and standard deviations without using a calculator.
Given the following data output: n = 12, min = 101, Q1 = 102, median = 134, Q3 = 160, max = 270. Which description of the data is best?
Given the following data output: n = 12, min = 101, Q1 = 102, median = 134, Q3 = 160, max = 270. Which description of the data is best?
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?
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?
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
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
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
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
If you are provided the five-number summary of: you can determine that 75% of the data exists between 23 and 30.
If you are provided the five-number summary of: you can determine that 75% of the data exists between 23 and 30.
Flashcards
Appropriate measures for skewed salary data
Appropriate measures for skewed salary data
Median and Interquartile Range (IQR) are better choices for skewed data than mean and standard deviation.
Combined class mean (2 classes)
Combined class mean (2 classes)
Calculate the weighted average of the means of two classes.
Time adjustments in cross-country
Time adjustments in cross-country
Adjust for a time error by adding the offset to each time.
Upper boundary calculation
Upper boundary calculation
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Skewed data recognition
Skewed data recognition
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Comparing IQR and Std Dev
Comparing IQR and Std Dev
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Data description: skewed and outlier
Data description: skewed and outlier
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New mean calculation (additional datapoint)
New mean calculation (additional datapoint)
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Stem-plot setup
Stem-plot setup
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Skewed right data example
Skewed right data example
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75% data range
75% data range
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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).
Studying That Suits You
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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.
