Podcast
Questions and Answers
A real estate company wants to understand housing prices in a specific neighborhood. They collect the prices of 11 recently sold houses. Which measure of central tendency would be MOST appropriate to use if there are a couple of houses that were significantly more expensive than the others?
A real estate company wants to understand housing prices in a specific neighborhood. They collect the prices of 11 recently sold houses. Which measure of central tendency would be MOST appropriate to use if there are a couple of houses that were significantly more expensive than the others?
- Mean
- Mode
- Median (correct)
- Range
A teacher records the scores of 20 students on a recent quiz. After calculating the measures of central tendency, they notice the mean is higher than the median. What does this suggest about the distribution of quiz scores?
A teacher records the scores of 20 students on a recent quiz. After calculating the measures of central tendency, they notice the mean is higher than the median. What does this suggest about the distribution of quiz scores?
- The distribution is bimodal.
- The distribution is symmetrical.
- The distribution is skewed to the left.
- The distribution is skewed to the right. (correct)
Consider two data sets: Set A (2, 4, 6, 8, 10) and Set B (2, 4, 6, 8, 10, 12). How does adding the number 12 to Set A to create Set B affect the mean and median?
Consider two data sets: Set A (2, 4, 6, 8, 10) and Set B (2, 4, 6, 8, 10, 12). How does adding the number 12 to Set A to create Set B affect the mean and median?
- Both the mean and median increase. (correct)
- Both the mean and median stay the same.
- The mean increases, and the median stays the same.
- The mean stays the same, and the median increases.
A store owner wants to analyze customer spending habits. They record the amount spent by each customer over a week. Which measure would be MOST useful for identifying the most common spending amount?
A store owner wants to analyze customer spending habits. They record the amount spent by each customer over a week. Which measure would be MOST useful for identifying the most common spending amount?
A meteorologist records the daily high temperatures for two weeks: Week 1 (70, 72, 74, 71, 73, 75, 76) and Week 2 (60, 62, 64, 61, 63, 65, 86). Which week likely has a larger range, and why?
A meteorologist records the daily high temperatures for two weeks: Week 1 (70, 72, 74, 71, 73, 75, 76) and Week 2 (60, 62, 64, 61, 63, 65, 86). Which week likely has a larger range, and why?
Consider a dataset with an even number of values. After arranging the dataset in ascending order, the two middle values are 25 and 30. What is the median of this dataset?
Consider a dataset with an even number of values. After arranging the dataset in ascending order, the two middle values are 25 and 30. What is the median of this dataset?
The median gas price in a city during July is calculated to be $3.50 per gallon. Which of the following is the most accurate interpretation of this median value?
The median gas price in a city during July is calculated to be $3.50 per gallon. Which of the following is the most accurate interpretation of this median value?
For a certain dataset, the mean and median are found to be very close in value. What does this similarity suggest about the distribution of the data?
For a certain dataset, the mean and median are found to be very close in value. What does this similarity suggest about the distribution of the data?
A dataset of student test scores is as follows: 75, 80, 80, 85, 90, 90, 90, 95. What is the mode of this dataset?
A dataset of student test scores is as follows: 75, 80, 80, 85, 90, 90, 90, 95. What is the mode of this dataset?
The daily high temperatures in a city for a week were recorded in degrees Fahrenheit. The highest temperature was 88°F and the lowest was 72°F. What is the range of temperatures for this week?
The daily high temperatures in a city for a week were recorded in degrees Fahrenheit. The highest temperature was 88°F and the lowest was 72°F. What is the range of temperatures for this week?
Flashcards
Mean
Mean
The arithmetic average of a data set, found by summing all values and dividing by the number of values.
Median
Median
The middle value in a data set when the values are arranged in ascending or descending order.
Mode
Mode
The value that appears most frequently in a data set.
Range
Range
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How to find the Median
How to find the Median
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What is the median?
What is the median?
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How to find the median with an even set?
How to find the median with an even set?
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What is the mode?
What is the mode?
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Multiple Modes
Multiple Modes
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What is the range?
What is the range?
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Study Notes
- The mean is the arithmetic average of a data set.
- To find the mean, add all the numbers in the data set, then divide by the number of values in the set.
- The median is the middle number in a data set when the numbers are listed in ascending or descending order.
- The mode is the value that appears most frequently in a data set.
- The range is the difference between the highest and lowest values in a data set.
Gasoline Prices in 2000
- Gasoline prices for each month of 2000, per the U.S. Bureau of Labor Statistics: 1.30, 1.37, 1.54, 1.51, 1.50, 1.62, 1.59, 1.51, 1.58, 1.56, 1.56, 1.49.
Mean
- The mean of a data set indicates the average value.
- To find the mean gas price for 2000, add all prices and divide by 12.
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- 30 + 1.37 + 1.54 + 1.51 + 1.50 + 1.62 + 1.59 + 1.51 + 1.58 + 1.56 + 1.56 + 1.49 = 18.13
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- 13 / 12 = 1.51
- The mean gas price for 2000 was $1.51.
Median
- The median represents the number that falls directly in the middle of the data set.
- Useful when one or two numbers are significantly larger or smaller than the rest.
- If numbers are close together, the mean and median will be similar.
- Arrange the numbers in ascending order: 1.30, 1.37, 1.49, 1.50, 1.51, 1.51, 1.54, 1.56, 1.56, 1.58, 1.59, 1.62
- Eliminate numbers from each end to find the middle.
- With an even set of numbers, there will be two numbers left in the middle so find the average of the two numbers.
- The two remaining numbers are 1.51 and 1.54
-
- 51 + 1.54 = 3.05
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- 05 / 2 = 1.53
- The median gas price is $1.53, meaning half of the prices are above and half are below this value.
Mode
- The mode indicates the most frequently occurring number in the data set.
- Two numbers appear twice: 1.51 and 1.56.
- The modes for this data set are $1.51 and $1.56.
Range
- The range shows the spread of the numbers in the data set.
- Find the range by subtracting the smallest number from the largest number.
-
- 62 - 1.30 = 0.32
- The range of gas prices in 2000 was $0.32.
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Description
Explore mean, median, mode, and range with a 2000 gasoline price data set. Learn how to calculate each measure. Understand how these statistical measures describe data.
