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IM Alg1.1.13 Lesson: More Standard Deviation

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Evaluate mentally.

Your teacher will assign you either a problem card or a data card from the applet below. Do not show or read your card to your partner.

If your teacher gives you the data card:If your teacher gives you the problem card:
  1. Silently read the information on your card.
  2. Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
  3. Before telling your partner the information, ask “Why do you need to know (that piece of information)?”
  4. Read the problem card, and solve the problem independently.
  5. Share the data card, and discuss your reasoning.
  1. Silently read your card and think about what information you need to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain to your partner how you are using the information to solve the problem.
  4. When you have enough information, share the problem card with your partner, and solve the problem independently.
  5. Read the data card, and discuss your reasoning.

Do not show or read your card to your partner.

For each situation, you are given two graphs of data, a measure of center for each, and a measure of variability for each.

  • Interpret the measure of center in terms of the situation.
  • Interpret the measure of variability in terms of the situation.
  • Compare the two data sets.
The heights of the 40 trees in each of two forests are collected.
mean: 44.8 feet, standard deviation: 4.72 feetmean: 56.03 feet, standard deviation: 7.87 feet


The number of minutes it takes Lin and Noah to finish their tests in German class is collected for the year.

mean: 29.48 minutes, standard deviation: 5.44 minutesmean: 28.44 minutes, standard deviation: 7.40 minutes


The number of raisins in a cereal with a name brand and the generic version of the same cereal are collected for several boxes. mean: 289.1 raisins, standard deviation: 19.8 raisins mean: 249.17 raisins, standard deviation: 26.35 raisins

One use of standard deviation is it gives a natural scale as to how far above or below the mean a data point is. This is incredibly useful for comparing points from two different distributions.

For example, they say you cannot compare apples and oranges, but here is a way. The average weight of a granny smith weighs 128 grams with a standard deviation of about 10 grams. The average weight of a navel orange is 140 grams with a standard deviation of about 14 grams. If we have a 148 gram granny smith apple and a 161 gram navel orange, we might wonder which is larger for its species even though they are both about 20 grams above their respective mean. We could say that the apple, which is 2 standard deviations above its mean, is larger for its species than the orange, which is only 1.5 standard deviations above its mean. How many standard deviations above the mean height of a tree in forest A is its tallest tree?

How many standard deviations above the mean height of a tree in forest A is its tallest tree?

Which tree is taller in its forest?

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