Grade: 9 Subject: Math (Statistics) Unit: Statistics Lesson: 3 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Guided Practice

Learning Objectives

In this guided practice lesson, you will:

Work through these 10 problems. Click each question to reveal the answer and explanation.

Question 1: Find the mean of: 12, 15, 18, 22, 23

Answer: Mean = 18

Solution: Sum = 12 + 15 + 18 + 22 + 23 = 90. Mean = 90 / 5 = 18.

Question 2: Find the median of: 7, 3, 9, 15, 11, 8, 4

Answer: Median = 8

Solution: Ordered: 3, 4, 7, 8, 9, 11, 15. The middle value (4th of 7) is 8.

Question 3: Find the range of: 45, 52, 38, 61, 47

Answer: Range = 23

Solution: Range = Maximum - Minimum = 61 - 38 = 23.

Question 4: Data set: 2, 4, 4, 5, 6, 8, 8, 8, 10. Find Q1, Q3, and IQR.

Answer: Q1 = 4, Q3 = 8, IQR = 4

Solution: Ordered data has median = 6. Lower half: 2, 4, 4, 5, so Q1 = 4. Upper half: 8, 8, 8, 10, so Q3 = 8. IQR = 8 - 4 = 4.

Question 5: The mean of 5 numbers is 24. Four of the numbers are 20, 22, 25, and 28. Find the fifth number.

Answer: The fifth number is 25.

Solution: Sum of 5 numbers = 24 x 5 = 120. Sum of four = 20 + 22 + 25 + 28 = 95. Fifth = 120 - 95 = 25.

Question 6: Find the mode(s) of: 3, 5, 5, 7, 8, 8, 8, 10, 12

Answer: Mode = 8

Solution: 8 appears 3 times, more than any other value. The mode is 8.

Question 7: A data set has mean 50 and standard deviation 8. A value of 66 is how many standard deviations above the mean?

Answer: 2 standard deviations above

Solution: z = (66 - 50) / 8 = 16 / 8 = 2 standard deviations above the mean.

Question 8: Data: 10, 12, 14, 16, 18. If each value is increased by 5, what happens to the mean and standard deviation?

Answer: Mean increases by 5; standard deviation stays the same.

Solution: Adding a constant shifts all values but doesn't change how spread out they are. New mean = 14 + 5 = 19.

Question 9: Which is more affected by outliers: mean or median?

Answer: Mean is more affected by outliers.

Solution: Mean uses all values in calculation, so extreme values pull it. Median only depends on the middle value(s).

Question 10: Data set A has IQR = 12 and Data set B has IQR = 5. Which set has more variability in the middle 50% of data?

Answer: Data set A has more variability.

Solution: A larger IQR means the middle 50% of data is more spread out. Set A (IQR = 12) has greater variability than Set B (IQR = 5).