Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
If your teacher gives you the data card:
For each situation, you are given two graphs of data, a measure of center for each, and a measure of variability for each.
The heights of the 40 trees in each of two forests are collected.
mean: 44.8 feet, standard deviation: 4.72 feetDot plot from 30 to 75 by 1's. Tree height in forest A in feet. Beginning at 30, number of dots above each increment is 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 4, 3, 4, 3, 3, 3, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.
mean: 56.03 feet, standard deviation: 7.87 feetDot plot from 30 to 75 by 1's. Tree height in forest B in feet. Beginning at 30, number of dots above each increment is 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3, 2, 1, 2, 2, 4, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0.
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 minutesDot plot from 10 to 44 by 1's. Time to finish test for Lin in minutes. Beginning at 10, number of dots above each increment is 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 3, 2, 1, 2, 1, 3, 1, 2, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0.
mean: 28.44 minutes, standard deviation: 7.40 minutesDot plot from 10 to 44 by 1's. Time to finish test for Noah in minutes. Beginning at 10, number of dots above each increment is 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 1, 3, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0.
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 raisinsHistogram from 200 to 330 by 10’s. Number of raisings in brand cereal. Beginning at 200 up to but not including 210, height of bar at each interval is 0, 0, 0, 0, 0, 3, 2, 3, 7, 7, 3, 2, 3, 0.
mean: 249.17 raisins, standard deviation: 26.35 raisinsHistogram from 200 to 330 by 10’s. Number of raisings in brand cereal. Beginning at 200 up to but not including 210, height of bar at each interval is 2, 3, 2, 4, 5, 4, 2, 3, 3, 2, 0, 0, 0, 0.
The more variation a distribution has, the greater the standard deviation. A more compact distribution will have a lesser standard deviation.
The first dot plot shows the number of points that a player on a basketball team made during each of 15 games. The second dot plot shows the number of points scored by another player during the same 15 games.
Dot plot from 1 to 17 by 1's. Points for player one. Beginning at 1, number of dots above each increment is 3, 2, 3, 1, 3, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0.
Dot plot from 1 to 17 by 1's. Points for player two. Beginning at 1, number of dots above each increment is 0, 3, 0, 2, 0, 3, 0, 1, 0, 3, 0, 0, 0, 1, 0, 2, 0.
The data in the first plot have a mean of approximately 3.87 points and standard deviation of about 2.33 points. The data in the second plot have a mean of approximately 7.73 points and a standard deviation of approximately 4.67 points. The second distribution has greater variability than the first distribution because the data are more spread out. This is shown in the standard deviation for the second distribution being greater than the standard deviation for the first distribution.
Standard deviation is calculated using the mean, so it makes sense to use it as a measure of variability when the mean is appropriate to use for the measure of center. In cases where the median is a more appropriate measure of center, the interquartile range is still a better measure of variability than standard deviation.