← MCAP Review  /  Review Packets  /  Statistics & Probability
⬇ Word (.docx)
Learning Goal: Measures of center (mean, median) tell what is typical; measures of variability (range, IQR, MAD) tell how spread out the data is.

Vocabulary

meanThe average: add all values, then divide by how many values there are.
medianThe middle value when the data is in order (average the two middle values if the count is even).
rangeThe largest value minus the smallest value.
interquartile range (IQR)Q3 minus Q1; the spread of the middle half of the data.
mean absolute deviation (MAD)The average distance of each value from the mean.

What You Need to Know

  • A SINGLE measure of center (mean or median) summarizes the whole data set with one typical value.
  • A SINGLE measure of variability (range, IQR, or MAD) summarizes how spread out the data is with one number.
  • Mean = sum of values ÷ number of values.
  • Median: put values in order, find the middle; for an even count, average the two middle values.
  • IQR: find the median, then Q1 (median of lower half) and Q3 (median of upper half); IQR = Q3 − Q1.
  • MAD: find the mean, then average how far each value is from the mean (use positive distances).

Worked Example I Do — watch how it works

Data: 4, 8, 6, 10, 2. Find the mean, median, and range.
  1. Step 1. Mean: 4+8+6+10+2 = 30, then 30 ÷ 5 = 6.
  2. Step 2. Median: order the values → 2,4,6,8,10; the middle value is 6.
  3. Step 3. Range: largest − smallest = 10 − 2 = 8.
Answer: Mean = 6, Median = 6, Range = 8.

Guided Practice We Do — try it together

  1. 1. Data: 4,6,9,11,15. Find the IQR.
    💡 Hint: Median is 9; lower half is 4,6 and upper half is 11,15.
  2. 2. Data: 2,4,6,8,10. The mean is 6. Find the MAD.
    💡 Hint: Distances from 6 are 4,2,0,2,4. Add them and divide by 5.
  3. 3. Data: 3,5,5,7,10. Find the mean and the median.
    💡 Hint: Sum is 30; the middle value in order is the 3rd one.

Independent Practice You Do — show your work

  1. 1. Data: 7,7,8,10,13. Find the mean.
  2. 2. Data: 12,15,11,14,18,10. Find the median.
  3. 3. Data: 5,9,12,4,20. Find the range.
  4. 4. Data: 3,5,7,8,12,14,18,20. Find the IQR.
  5. 5. Data: 1,3,5,7,9. The mean is 5. Find the MAD.

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.SP.A.3.
Item 1Selected Response6.SP.A.3

Which of these is a measure of variability (spread)?

Select the correct answer.

Item 2Selected Response6.SP.A.3

Data: 6, 10, 8, 12, 4. What is the mean?

Select the correct answer.

Item 3Constructed Response6.SP.A.3

Data: 2, 5, 5, 8, 10. Find the median and the range.

Enter your answer in the space provided. Show your work.

Enter your answer:
Teacher Answer Key (click to show)
Independent 1Mean = 45 ÷ 5 = 9.
Independent 2Order: 10,11,12,14,15,18; median = (12+14)/2 = 13.
Independent 3Range = 20 − 4 = 16.
Independent 4Median = 10, Q1 = 6, Q3 = 16, IQR = 10.
Independent 5Distances 4,2,0,2,4 sum to 12; MAD = 2.4.
Item 1 · 6.SP.A.3D — The IQR measures spread; mean, median, and mode are measures of center.
Item 2 · 6.SP.A.3A — 6+10+8+12+4 = 40, and 40 ÷ 5 = 8.
Item 3 · 6.SP.A.3Median = 5, Range = 8. — In order 2,5,5,8,10 the middle value is 5; range = 10 − 2 = 8.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.SP.A.3