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What is the difference between mean, median, and mode?
What is the difference between mean, median, and mode?
- Mean is the sum of all values divided by the number of values; median is the middle value in a set of data; mode is the most frequently occurring value in a set (correct)
- Mean is the average of the largest and smallest values in a set of data; median is the most frequently occurring value in a set; mode is the middle value in a set of data
- Mean is the middle value in a set of data; median is the sum of all values divided by the number of values; mode is the most frequently occurring value in a set
- Mean is the most frequently occurring value in a set; median is the sum of all values divided by the number of values; mode is the middle value in a set of data
Why might the numerical average be misleading?
Why might the numerical average be misleading?
- When there are no clear patterns or trends in the data set
- When there is an equal distribution of values across the data set
- When there is a small elite with extremely high incomes in a population, while most people have very low incomes (correct)
- When there are too many outliers in the data set
What does 'range' express in statistics?
What does 'range' express in statistics?
- The difference between the largest and smallest values in a data set (correct)
- The average of all values in a data set
- The sum of all values in a data set
- The frequency of occurrence for each value in a data set
Why might a different sort of average be used to express income instead of numerical average?
Why might a different sort of average be used to express income instead of numerical average?
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Why do we need different kinds of averages according to the text?
Why do we need different kinds of averages according to the text?
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Study Notes
Mean, Median, and Mode
- Mean is the most common form of average, calculated by adding up all the values in a set and dividing by the number of values
- Median is the middle value in a set of numbers, after they are arranged in order from least to greatest
- Mode is the most frequent value in a set of numbers. There can be more than one mode
When the Mean is Misleading
- The numerical average (mean) can be misleading if there are outliers or extreme values in the set.
- These extreme values can disproportionately influence the mean, making it seem higher or lower than it actually represents the majority of the data.
Range
- Range tells us the spread of data in a dataset.
- The range is calculated by subtracting the smallest value from the largest value.
Income Averages
- A different average, such as the median, might be a more accurate reflection of income than the mean.
- This is because the mean income can be skewed by the presence of a small number of high earners.
- The median income provides a better representation of the typical income level in a population, as it is not influenced by extreme values.
Different Averages
- We may need different kinds of averages depending on the nature of the data and the purpose of the analysis.
- The mean is a good measure for data that is normally distributed and does not have any outliers.
- The median is a better choice for data that is skewed or contains outliers, and it is typically used to represent income.
- The mode can be useful for identifying the most common value in a dataset.
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