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Cogito

Probability and Statistics · Chapter 2 · Lesson 2

Practice Worksheet

Range, Variance, and Standard Deviation

How far from typical is typical?

12 problems · about 22 minutes · TEKS P.S.1.D, S-ID.A.2

NameDate

Figure — use these to answer the problems

Pull the values apart and the box widens. Bunch them and it narrows. That is spread.
020
  • Minimum8
  • Lower quartile8.50
  • Median10
  • Upper quartile11.50
  • Maximum12
  • Interquartile range3
Value 18
Value 29
Value 310
Value 411
Value 512
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Variance is 36. What is the standard deviation?

    Answer

  2. Why are deviations squared?

    • Otherwise the positives and negatives cancel to zero.
    • To make the numbers larger.

  3. Data 5, 9, 14. Range?

    Answer

  4. Variance is 25. What is the standard deviation?

    Answer

  5. Standard deviation is 7. What is the variance?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Data 4, 4, 4. Standard deviation?

    Answer

  2. Mean 10, one value 13. What is that deviation?

    Answer

  3. What do all the deviations from the mean add up to?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the standard deviation calculation in order.

    Write 1 to 4 in the boxes to put these in order.

    • Find the mean.
    • Subtract the mean from each value.
    • Square the deviations and average them.
    • Take the square root.

  2. Variance 100. Standard deviation?

    Answer

  3. The Range

    Data 3, 8, 15, 20. What is the range?

    Answer

  4. The Identical Set

    Data 6, 6, 6, 6. What is the standard deviation?

    Answer