Mathematics
Grade 8
15 min
Calculate mean, median, mode, and range
Calculate mean, median, mode, and range
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1
Introduction & Learning Objectives
Learning Objectives
Define mean, median, mode, and range.
Calculate the mean of a given data set.
Determine the median of a given data set, including sets with an even number of values.
Identify the mode(s) of a given data set.
Compute the range of a given data set.
Interpret what each measure tells us about the data.
Choose the most appropriate measure of central tendency for a given context.
Ever wonder how your test scores compare to the rest of the class? 📊 Or how a company decides the 'average' salary? Let's find out!
In this lesson, you'll learn how to calculate four important statistical measures: mean, median, mode, and range. These tools help us understand and summarize data, making sense of large sets of numbers in everyday life.
Real-World...
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Key Concepts & Vocabulary
TermDefinitionExample
Data SetA collection of numbers or values that represent information about something.The ages of students in a class: {13, 14, 13, 15, 14}
Measure of Central TendencyA single value that attempts to describe a set of data by identifying the central position within that set of data. (Mean, Median, Mode are examples)If most students scored around 80% on a test, 80% would be a measure of central tendency.
MeanThe arithmetic average of a data set. It is calculated by summing all values and dividing by the number of values.For {2, 4, 6}, the mean is (2+4+6)/3 = 12/3 = 4.
MedianThe middle value in a data set when the values are arranged in order from least to greatest. If there's an even number of values, it's the average of the two middle values.For {1, 3, 5, 7,...
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Core Formulas
Mean Formula
$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$
To find the mean, add up all the numbers in your data set, then divide that sum by the total count of numbers in the set.
Median Rule
1. Order the data from least to greatest.\n2. If there is an odd number of values, the median is the single middle value.\n3. If there is an even number of values, the median is the average of the two middle values.
The median is the 'middle' number. Always sort your data first before finding the middle.
Mode Rule
Identify the value(s) that appear most frequently in the data set. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode (if all values appear with the same frequency).
The mode is the number that shows u...
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Challenging
A real estate agent is listing house prices for a neighborhood. The prices are: $250,000, $275,000, $300,000, $260,000, and $1,500,000. Which measure of central tendency would be the most appropriate to describe the 'typical' house price?
A.Mean, because it is the most accurate.
B.Median, because it is not heavily influenced by the extreme high price.
C.Mode, because it shows the most common price.
D.Range, because it shows the spread of prices.
Challenging
The mean of 5 numbers is 12. Four of the numbers are 10, 15, 7, and 18. What is the fifth number?
A.10
B.12
C.8
D.14
Challenging
A data set has a mean of 30 and a range of 20. If every number in the data set is doubled, what are the new mean and range?
A.New mean is 30, new range is 20
B.New mean is 60, new range is 20
C.New mean is 30, new range is 40
D.New mean is 60, new range is 40
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