Grade: Grade 7 Subject: Mathematics Unit: Statistics Lesson: 3 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Guided Practice: Statistics

Learn

In this guided practice lesson, you'll work through statistical problems step-by-step, building confidence with measures of center, measures of variability, and data comparison.

Key Concepts Review

  • Mean: The average of a data set (sum of values divided by count)
  • Median: The middle value when data is ordered from least to greatest
  • Mode: The value that appears most frequently
  • Range: The difference between the maximum and minimum values
  • Mean Absolute Deviation (MAD): The average distance of each data point from the mean
  • Interquartile Range (IQR): The range of the middle 50% of data (Q3 - Q1)

When to Use Each Measure

Choose the median when your data has outliers or is skewed. Choose the mean when your data is symmetric without extreme values. The MAD and IQR help you understand how spread out your data is.

Examples

Example 1: Finding the Mean and Median

Problem: A basketball player scored the following points in 7 games: 12, 15, 18, 14, 22, 16, 15. Find the mean and median.

Step 1: Find the mean

Sum = 12 + 15 + 18 + 14 + 22 + 16 + 15 = 112

Mean = 112 / 7 = 16 points

Step 2: Find the median

Order the data: 12, 14, 15, 15, 16, 18, 22

The middle value (4th value) is 15

Median = 15 points

Example 2: Calculating Mean Absolute Deviation

Problem: Find the MAD for this data set: 4, 6, 8, 10, 12

Step 1: Find the mean

Mean = (4 + 6 + 8 + 10 + 12) / 5 = 40 / 5 = 8

Step 2: Find the distance from each value to the mean

|4 - 8| = 4, |6 - 8| = 2, |8 - 8| = 0, |10 - 8| = 2, |12 - 8| = 4

Step 3: Find the mean of the distances

MAD = (4 + 2 + 0 + 2 + 4) / 5 = 12 / 5 = 2.4

Example 3: Comparing Two Data Sets

Problem: Class A test scores: 70, 75, 80, 85, 90 (Mean = 80). Class B test scores: 60, 70, 80, 90, 100 (Mean = 80). Which class has more consistent scores?

Step 1: Calculate the range for each class

Class A Range = 90 - 70 = 20

Class B Range = 100 - 60 = 40

Step 2: Interpret the results

Class A has more consistent scores because the range is smaller (20 vs 40), meaning scores are closer together.

Practice

Work through these problems. Show your steps for full understanding.

Problem 1: The heights (in inches) of 6 students are: 58, 62, 60, 65, 59, 64. Find the mean and median height.

Problem 2: A student's quiz scores are: 85, 92, 78, 88, 92, 90, 85. Find the mode(s) of the data.

Problem 3: Calculate the range for this data set: 23, 45, 67, 34, 56, 78, 12

Problem 4: Find the MAD for: 10, 12, 14, 16, 18

Problem 5: Two groups measured their running times (in seconds): Group X: 45, 48, 50, 52, 55. Group Y: 40, 45, 50, 55, 60. Which group has more variability in their times? Explain using range.

Problem 6: The data set 12, 15, 18, 21, 24, 27 has a mean of 19.5. If we add the value 19 to the data set, will the new mean be higher, lower, or the same as 19.5?

Problem 7: A store recorded daily sales: $150, $200, $175, $180, $195, $800, $190. Should you use the mean or median to describe typical daily sales? Explain why.

Problem 8: Order this data set and find Q1, Q2 (median), and Q3: 28, 35, 42, 19, 56, 48, 31, 22, 45

Problem 9: Calculate the IQR for the data in Problem 8.

Problem 10: A sample of 5 test scores has a mean of 82. If four of the scores are 78, 85, 80, and 90, what is the fifth score?

Check Your Understanding

Answer these questions to verify your mastery of the concepts.

  1. What is the difference between mean and median?
  2. When is the median a better measure of center than the mean?
  3. How does MAD help us understand a data set?
  4. If two data sets have the same mean but different ranges, what does that tell you?
  5. What does a larger IQR indicate about the spread of data?

Next Steps

  • Review any problems where you made errors
  • Practice calculating MAD and IQR until it feels automatic
  • Move on to Word Problems to apply these skills in real-world contexts