Mathematics
Grade 5
15 min
Find the missing number: mean, median, mode, and range
Find the missing number: mean, median, mode, and range
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1
Introduction & Learning Objectives
Learning Objectives
Define mean, median, mode, and range for a given data set.
Calculate the mean, median, mode, and range for a set of numbers.
Determine a missing number in a data set when the mean is provided.
Determine a missing number in a data set when the median or mode is provided.
Determine a missing number in a data set when the range is provided.
Apply their understanding of these statistical measures to solve simple real-world problems.
Ever wonder how a sports coach figures out the 'average' score of their team, or how a store knows which toy is the most popular? 🤔 It's all about understanding numbers!
In this lesson, you'll learn about four important ways to describe a group of numbers: mean, median, mode, and range. You'll also becom...
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Key Concepts & Vocabulary
TermDefinitionExample
Data SetA collection of numbers or information gathered about something.The ages of students in a club: {10, 11, 10, 12, 11}
MeanThe average of a set of numbers. You find it by adding all the numbers together and then dividing by how many numbers there are.For {2, 4, 6}, the mean is (2+4+6) / 3 = 12 / 3 = 4.
MedianThe middle number in a data set when the numbers are arranged in order from least to greatest. If there are two middle numbers, the median is the average of those two.For {2, 3, 5, 8, 9}, the median is 5. For {2, 3, 5, 8}, the median is (3+5)/2 = 4.
ModeThe number that appears most often in a data set. A data set can have one mode, many modes, or no mode.For {2, 3, 3, 5, 7}, the mode is 3. For {1, 2, 3, 4}, there is no mode.
RangeThe difference between the...
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Core Formulas
Calculating the Mean
$\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}$
Use this rule to find the average value of a data set. Add all the numbers, then divide by how many numbers you added.
Calculating the Range
$\text{Range} = \text{Highest number} - \text{Lowest number}$
Use this rule to find how spread out the numbers in a data set are. Always subtract the smallest number from the largest number.
Finding a Missing Number (Mean)
$\text{Missing Number} = (\text{Mean} \times \text{Count of numbers}) - \text{Sum of known numbers}$
If you know the mean and all but one number, you can work backward. First, find the total sum the numbers *should* add up to, then subtract the sum of the numbers you already know.
Finding a Missing Number (Range)...
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Challenging
A set of five numbers {15, 25, 18, x, y} has a mean of 20 and a range of 12. If x is the smallest number in the set, what is the value of y?
A.27
B.15
C.29
D.42
Challenging
The scores on four of five quizzes are 7, 8, 9, and 10. The mean of all five quizzes is the same as the median. What is the smallest possible whole number score for the fifth quiz?
A.8
B.6
C.9
D.11
Challenging
A data set is {10, 14, x, 20, 22}. The mean of the set is 2 greater than its median. If x is less than 20, what is the value of x?
A.16
B.12
C.18
D.14
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