🟠 Level 0 — Most Support. Same skills as Level 1, with extra help: press then tap any text to hear it. Open every 💡 Hint — that is okay here.

Reveal Math · Unit 2 · Supplemental

Statistics & Data

Extra support and enrichment for statistical questions, data displays, measures of center (mean, median, mode), measures of variation, and data interpretation. Standards 6.SP.A.1, 6.SP.B.5.

🖨️ Differentiated Practice Worksheets

Ready-to-print practice at three levels — pick the right fit for each student.

Level 0 · Extra Support Scaffolded steps, worked examples, extra space. Level 1 · Support Guided practice on the core skills. Level 2 · Enrichment Stretch problems and deeper reasoning.

Visual Vocabulary

How many pets do students have? ?
Statistical Question
Pregunta estadistica
A question where the answers will be different (vary). Example: "How tall are the students in our class?"
3, 5, 5, 7, 8 data
Data
Datos
Numbers or information you collect. Example: the test scores of every student.
add all, then divide 5.6 average
Mean
Media / Promedio
The average. Add all the numbers, then divide by how many numbers there are.
2 4 6 8 10 middle number
Median
Mediana
The middle number when data is in order from least to greatest.
2 4 7 7 9 most common
Mode
Moda
The number that appears the most in a data set. There can be more than one mode.
dot plot
Dot Plot
Diagrama de puntos
A graph with dots stacked above a number line. Each dot is one piece of data.
Histogram
Histograma
A bar graph that shows how often data falls in different ranges (intervals). Bars touch each other.
max min range = max - min
Range
Rango
The difference between the biggest and smallest number. Range = Maximum - Minimum.

Sentence Frames

This is a statistical question because the answers will  .
The mean of the data is   because I added   and divided by  .
The median is   because it is the   number when the data is in order.
The mode is   because it appears   times, more than any other number.
The range is   because   minus   equals  .
The data is spread out / clustered because  .

Step-by-Step Visual Guides

How to Find the Mean (Average)

Data: 4, 8, 6, 10, 7

1 Add all the numbers together: 4 + 8 + 6 + 10 + 7 = 35
↓
2 Count how many numbers there are: 5 numbers
↓
3 Divide the total by the count: 35 / 5 = 7
↓
4 Check: The mean (7) should be between the smallest (4) and largest (10). It is!

How to Find the Median (Middle Number)

Data: 12, 5, 9, 3, 8, 15, 7

1 Order the numbers from least to greatest: 3, 5, 7, 8, 9, 12, 15
↓
2 Count the numbers: 7 values (odd number)
↓
3 Find the middle: Cross off one from each end: 3, 5, 7, 8, 9, 12, 15. The 4th number is 8.
↓
! Even count? If there are 6 numbers, find the two middle numbers and take their average. Example: 3, 5, 7, 8, 9, 12 → (7+8)/2 = 7.5

How to Read a Dot Plot

1 Look at the number line on the bottom — these are the data values.
↓
2 Each dot above a number means one data point. Count the dots to find the frequency.
↓
3 The tallest stack shows the mode. Look for clusters (groups) and gaps (empty spaces).

Simplified Practice

  1. Is this a statistical question? "How old is the principal?" (Yes or No)
    A statistical question expects different answers from different people or sources. Does this question have just one answer?
    No. The principal has one specific age, so there is no variation in the answer.
  2. Is this a statistical question? "How many siblings do students in our class have?"
    Will different students give different answers?
    Yes! Different students have different numbers of siblings, so the answers vary.
  3. Find the mean: 3, 5, 7, 9, 6
    Add all the numbers: 3 + 5 + 7 + 9 + 6 = ? Then divide by 5 (there are 5 numbers).
    30 / 5 = 6. The mean is 6.
  4. Find the median: 2, 8, 4, 10, 6
    First put them in order: 2, 4, 6, 8, 10. Then find the middle number.
    In order: 2, 4, 6, 8, 10. The middle (3rd) number is 6. The median is 6.
  5. Find the mode: 4, 7, 2, 7, 5, 3, 7, 5
    Count how many times each number appears. Which number shows up the most?
    7 appears 3 times (more than any other number). The mode is 7.
  6. Find the range: 15, 22, 8, 31, 12
    Range = biggest number - smallest number. What is the biggest? The smallest?
    Biggest: 31. Smallest: 8. Range = 31 - 8 = 23.
  7. Find the median: 10, 4, 8, 6, 12, 2
    Order them first: 2, 4, 6, 8, 10, 12. There are 6 numbers (even!), so find the two middle numbers and average them.
    In order: 2, 4, 6, 8, 10, 12. The two middle numbers are 6 and 8. Median = (6 + 8) / 2 = 7.
  8. A dot plot shows: 3 dots above 5, 1 dot above 6, 4 dots above 7, 2 dots above 8. How many data points total? What is the mode?
    Add all the dots: 3 + 1 + 4 + 2. The mode is the value with the most dots.
    Total: 3 + 1 + 4 + 2 = 10 data points. Mode: 7 (it has 4 dots, the most).
  9. Test scores: 80, 90, 70, 85, 95. Find the mean and the range.
    Mean: add all scores, divide by 5. Range: biggest minus smallest.
    Mean: (80 + 90 + 70 + 85 + 95) / 5 = 420 / 5 = 84. Range: 95 - 70 = 25.
  10. Which measure of center changes the most if you add one very large number (an outlier) to a data set: mean or median?
    Think about what happens to the sum when you add a very big number. Does the middle position change a lot?
    The mean changes the most. An outlier is added into the total, which pulls the mean up (or down). The median stays near the center because it only depends on position, not value.

Real-World Connections

Sports Stats

Basketball players track points per game. If a player scores 12, 18, 15, 22, and 8, the coach finds the mean (15) to see the average performance and the range (14) to see how consistent the player is.

Weather Forecasting

Weather stations collect daily temperatures. The mean temperature for a week tells you the typical temperature. A big range means the weather changed a lot!

A B+ A- B A

Report Cards

Teachers use the mean of your test scores to calculate your grade. If your scores are 85, 90, 78, and 92, your average is (85+90+78+92)/4 = 86.25. That is your overall grade!

Screen Time

You track how many minutes you spend on your phone each day for a week. Finding the median helps you know your typical day — it is not pulled up by one day you used your phone a lot.

Challenge Problems

  1. The mean of five numbers is 12. Four of the numbers are 10, 15, 8, and 14. What is the fifth number? Medium
    If the mean is 12 and there are 5 numbers, the total must be 12 x 5 = 60. Subtract the four known numbers.
    Total = 12 x 5 = 60. Known sum = 10 + 15 + 8 + 14 = 47. Fifth number = 60 - 47 = 13.
  2. A data set has a median of 20 and a mean of 25. Explain how this is possible. Give an example of 5 numbers that fit. Medium
    The mean is bigger than the median. That happens when there are large outliers pulling the mean up.
    Example: 10, 15, 20, 25, 55. Median = 20 (middle). Mean = (10+15+20+25+55)/5 = 125/5 = 25. The outlier 55 pulls the mean above the median.
  3. Create a data set of 6 numbers where the mean is 10, the median is 9, and the mode is 8. Hard
    Total must be 60 (mean 10 x 6 numbers). Mode is 8, so use 8 at least twice. Median of 6 numbers = average of 3rd and 4th values = 9.
    One answer: 5, 8, 8, 10, 13, 16. Check: Sum = 60, mean = 10. Ordered: 5,8,8,10,13,16. Median = (8+10)/2 = 9. Mode = 8.
  4. A student's test scores are 72, 85, 91, 68, and 79. She has one more test. What score does she need to get a mean of 80? Medium
    With 6 tests and a mean of 80, the total must be 80 x 6 = 480. Subtract the sum of the first 5 tests.
    Needed total: 480. Current sum: 72+85+91+68+79 = 395. Needed score: 480 - 395 = 85.
  5. Two classes took the same test. Class A (20 students) had a mean of 78. Class B (30 students) had a mean of 84. What is the overall mean for all 50 students? Hard
    You cannot just average 78 and 84 because the classes have different sizes. Find the total points for each class first.
    Class A total: 20 x 78 = 1,560. Class B total: 30 x 84 = 2,520. Combined: (1,560 + 2,520) / 50 = 4,080 / 50 = 81.6.
  6. A histogram shows: 0-10 (frequency 3), 10-20 (frequency 7), 20-30 (frequency 12), 30-40 (frequency 5), 40-50 (frequency 3). Estimate the mean of the data. Hard
    Use the midpoint of each interval: 5, 15, 25, 35, 45. Multiply each midpoint by its frequency, add them, and divide by total frequency.
    Sum = (5x3)+(15x7)+(25x12)+(35x5)+(45x3) = 15+105+300+175+135 = 730. Total frequency = 30. Estimated mean = 730/30 = 24.3.
  7. Removing one number from the set {4, 6, 7, 9, 10, 12, 15} changes the mean from 9 to 9.5. Which number was removed? Hard
    Original sum = 9 x 7 = 63. After removing one number, there are 6 numbers with mean 9.5, so new sum = 9.5 x 6 = 57.
    Removed number = 63 - 57 = 6.
  8. A dot plot shows quiz scores: two 6s, three 7s, five 8s, four 9s, and one 10. Find the mean, median, and mode. Medium
    Total values = 2+3+5+4+1 = 15. Sum = (6x2)+(7x3)+(8x5)+(9x4)+(10x1). Median is the 8th value.
    Sum = 12+21+40+36+10 = 119. Mean = 119/15 = 7.93. In order, the 8th value is 8. Median = 8. Mode = 8 (highest frequency of 5).
  9. True or false: A data set can have a mean of 50 and every value in the set is less than 50. Explain. Expert
    Think: if every value is less than 50, what is the maximum possible average?
    False. If every value is less than 50, the sum divided by the count must also be less than 50. The mean can only equal 50 if at least one value is 50 or greater.
  10. Design a data set of 8 values where the mean, median, and mode are all equal to 15. Expert
    The total must be 15 x 8 = 120. Use 15 at least twice for the mode. The 4th and 5th values must average to 15 for the median.
    One answer: 10, 12, 14, 15, 15, 16, 18, 20. Sum = 120, mean = 15. Median = (15+15)/2 = 15. Mode = 15.

Real-World Investigations

Classroom Survey & Analysis

Design and conduct a statistical investigation about your classmates.

  1. Write a statistical question (e.g., "How many hours of sleep did you get last night?")
  2. Collect data from at least 20 classmates
  3. Create a dot plot AND a histogram of the data
  4. Calculate the mean, median, mode, and range
  5. Write a paragraph describing what the data shows — mention clusters, gaps, and outliers
  6. Explain which measure of center best represents the data and why

Does Practice Make Perfect?

Investigate whether practice time affects performance using data you collect.

  1. Choose a simple skill (free throws, typing speed, paper airplane distance)
  2. Record 10 attempts on Day 1 and calculate the mean
  3. Practice for 15 minutes each day for 5 days
  4. Record 10 more attempts and calculate the new mean
  5. Compare the two data sets: means, medians, and ranges
  6. Write a conclusion: Did practice improve performance? How do the statistics show it?

Media Fact Check

Find a news article that uses statistics (average salary, test scores, etc.) and analyze whether the data is presented fairly.

  1. Find an article that states an average or other statistical claim
  2. Identify which measure of center was used (mean, median, or mode)
  3. Discuss: could a different measure tell a different story?
  4. Look for: Is the sample size given? Could there be outliers?
  5. Write your own fair summary of what the data actually shows

Brain Teasers

The Disappearing Mean

Five friends have a mean height of 60 inches. When a sixth friend joins, the mean drops to 58 inches. How tall is the sixth friend?

Original total: 5 x 60 = 300 inches. New total: 6 x 58 = 348 inches. Sixth friend: 348 - 300 = 48 inches (4 feet tall).

Same Mean, Different Data

Find two different data sets of 4 numbers each that both have a mean of 20 and a range of 10, but different medians.

Set 1: 15, 18, 22, 25. Mean = 80/4 = 20, Range = 10, Median = 20. Set 2: 15, 16, 24, 25. Mean = 80/4 = 20, Range = 10, Median = 20. Actually try: Set 1: 15, 19, 21, 25. Median = 20. Set 2: 15, 17, 23, 25. Median = 20. Hmm — with range 10 (min 15, max 25), we need two middle numbers summing to 40. Try: Set A: 15, 20, 20, 25 (median = 20). Set B: 15, 15, 25, 25 (median = 20). Same median again. This is tricky because range = max - min constrains us. Answer: it is very hard when range is fixed — great discovery!

The Tricky Outlier

Data set: 10, 12, 11, 13, 12, 11, 100. Without calculating, which measure of center would you use to describe the "typical" value, and why?

Use the median (12). The outlier (100) would pull the mean way up to about 24.1, which does not represent the typical value. The median ignores extreme values and stays near the cluster of 10-13.

The Impossibility Puzzle

Can a data set of 5 whole numbers have a mean of 10, a median of 10, and a range of 0? If yes, give an example. If no, explain why.

Yes! If the range is 0, all numbers are the same. The set {10, 10, 10, 10, 10} has mean = 10, median = 10, and range = 0.

Extension Topics

Where This Leads: Sampling & Bias

In 7th grade, you will learn how the way you collect data matters. Surveying only your friends gives biased data. Random sampling gives results that represent the whole population. Understanding mean, median, and mode now prepares you to evaluate whether data is trustworthy.

Where This Leads: Probability

Statistics and probability are closely connected. Once you understand how data is distributed, you can start predicting outcomes. If the mean score on a test is 80 with a small range, you can predict most students scored near 80. This leads to probability distributions in high school.

Where This Leads: Interquartile Range (IQR)

The range can be misleading if there are outliers. In 7th grade, you will learn about quartiles (Q1, Q2, Q3) and the IQR, which measures the spread of the middle 50% of data. You will also learn to build box plots, which show the five-number summary visually.

Self-Assessment

Rate your confidence: 1 = Need help, 2 = Getting there, 3 = Got it, 4 = Can teach it

  • I can tell if a question is a statistical question
  • I can calculate the mean of a data set
  • I can find the median (including with an even number of values)
  • I can identify the mode and range
  • I can read and interpret a dot plot
  • I can read and interpret a histogram
  • I can explain how outliers affect the mean vs. median
  • I can choose the best measure of center for a data set