🔢 MathGrade 6Lesson 26
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Mean, Median, Mode and Range

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Learning Objectives

  • 1Calculate the mean of a data set by adding all values and dividing by the count
  • 2Find the median by sorting the data and selecting the middle value
  • 3Identify the mode as the value that appears most often
  • 4Compute the range by subtracting the smallest value from the largest
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Mini Lesson

A data set is just a list of numbers — game scores, heights, daily temperatures, the number of pets each kid in your neighborhood owns. Once you have a data set, four simple measures help you describe it: mean, median, mode, and range. Each one answers a different question about the data. Together they give you a quick portrait of what is typical, what is in the middle, what is most common, and how spread out the values are.

Mean (the average)

  • Mean tells you the AVERAGE value in the data set.
  • Step 1: add ALL the values together to get a total (the sum).
  • Step 2: divide the sum by the COUNT (how many values there are).
  • Formula: Mean = sum / count.
  • Example: 4, 7, 8, 8, 12. Sum = 4 + 7 + 8 + 8 + 12 = 39. Count = 5. Mean = 39 / 5 = 7.8.
  • Tip: the mean does not have to be one of the original numbers — 7.8 is not in the data set.

Median (the middle)

  • Median is the MIDDLE value when the data is sorted from smallest to largest.
  • Step 1: sort the data in order.
  • Step 2: cross off pairs from each end until one value (or two) is left in the middle.
  • If there is an ODD count, the median is the single middle value.
  • If there is an EVEN count, the median is the AVERAGE of the two middle values.
  • Example (odd): 4, 7, 8, 8, 12 -> middle value is 8 -> Median = 8.
  • Example (even): 2, 4, 6, 10 -> two middles are 4 and 6 -> Median = (4 + 6) / 2 = 5.

Mode (the most common)

  • Mode is the value that appears MOST OFTEN in the data set.
  • Step 1: count how many times each value appears.
  • Step 2: pick the one with the highest count.
  • A data set can have ONE mode, TWO modes (bimodal), or NO mode if every value appears the same number of times.
  • Example: 4, 7, 8, 8, 12 -> 8 appears twice, the rest appear once -> Mode = 8.
  • Example (no mode): 1, 2, 3, 4 -> every value appears once -> No mode.

Range (the spread)

  • Range tells you HOW SPREAD OUT the data is.
  • Formula: Range = largest value - smallest value.
  • Example: 4, 7, 8, 8, 12 -> largest is 12, smallest is 4 -> Range = 12 - 4 = 8.
  • A small range means the data is close together. A large range means it is spread out.
Data on a Number LineA number line from 0 to 14 with the data set 4, 7, 8, 8, 12 plotted as dots. Mean 7.8 is marked with a dashed line, median and mode at 8 with a solid line, and a range bracket from 4 to 12.Data: 4, 7, 8, 8, 12Mean 7.8. Median 8. Mode 8. Range 8.01234567891011121314Mean 7.8Median = Mode = 8Range = 12 - 4 = 8Mean = sum / count = 39 / 5 = 7.8Sort the data first. Then read each measure off the line.
Plot the data, then read each measure.
Mean, Median, Mode, RangeFour labeled rows defining each measure with a tiny example: Mean (add then divide), Median (middle when sorted), Mode (most often), Range (largest minus smallest).Mean . Median . Mode . RangeFour measures of a data set.MEANAdd all values, then divide by how many.4 + 7 + 8 + 8 + 12 = 39, 39 / 5 = 7.8MEDIANMiddle value when the data is sorted.4, 7, [8], 8, 12 -> Median = 8MODEValue that appears most often.8 appears twice -> Mode = 8RANGELargest minus smallest.12 - 4 = 8 -> Range = 8Sort the data first. Then read each measure.
Each measure answers a different question.
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Tip: ALWAYS sort the data first. Sorting makes the median, mode, and range easy to read straight off the list. Mean is the only one where order does not matter — but sorting still helps you spot duplicates.

Vocabulary
data set
A collection of numbers gathered from observations or measurements.
mean
The average; sum of all values divided by the count of values.
median
The middle value of a data set after the values are sorted.
mode
The value that occurs most often in a data set; can be one, several, or none.
range
The difference between the largest and smallest values in a data set.
sum
The total when all the values in a data set are added together.
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← Lesson 25: Collect and Organize Data SetsLesson 27: Histograms and Box Plots →