Measures of Center

Key Concept You can compare two data sets by comparing their individual data values. A quicker way to make a general comparison of two data sets is to compare their measures of center.

Examples A biology student is studying two species of endangered parrots. What is the median wingspan of each sample? Make a comparative inference based on the median values.

Examples There are two samples in this study. The sample of Hyacinth Macaws and the sample of Kakapos. When seen side by side and on different scales, it can be difficult to compare data displays. You can line up the box plots one over the other on the same scale to get a better idea of where the quartiles fall in comparison to each other. Extend the scale of the Hyacinth Macaw box plot so that both plots can be seen on one scale. Change the title to reflect that the new box plot shows the samples of both endangered parrots. The line in the center of each box is the median.

Examples The median wingspan of the Hyacinth Macaw sample is greater than the median wingspan of the Kakapo sample. From the median value of each sample, you can infer that the Hyacinth Macaw population generally has a greater wingspan than the Kakapo population.

Examples A book publisher is testing two versions of a new book. A random sample of people are given 30 minutes to read each version. What is the median of each sample?

Examples Make a comparative inference based on the median values. The median number of pages read of Version A is great than the median number of pages read of Version B in the same amount of time. You could infer that Version A is easier to read than Version B.

Examples A biology student is studying two species of endangered parrots. What is the mean weight of each sample? Make a comparative inference based on the mean values. Hyacinth Macaw Sample (lb): 2.8, 3.7, 3.9, 3.0, 3.1, 3.4, 2.9, 3.2 Kakapo Sample (lb): 3.9, 4.5, 5.3, 6.7, 7.4, 8.1, 6.4, 8.1

Examples Hyacinth Macaw Sample Mean: (2.8, 3.7, 3.9, 3.0, 3.1, 3.4, 2.9, 3.2)/8 =3.25 lb Kakapo Sample Mean: (3.9, 4.5, 5.3, 6.7, 7.4, 8.1, 6.4, 8.1)/8 = 6.3 lb COMPARATIVE INFERENCE: Hyacinth Macaws generally weigh less or are lighter than Kakapos. Kakapos generally weigh more or are heavier than Hyacinth Macaws.

Examples A book publisher is testing two versions of a new book. A random sample of people is given 30 minutes to read each version. What is the mean of each sample? Make a comparative inference based on the mean values.

Examples Version A Mean: 20+20+24+24+25+25+25+25+26+26+26+27 12 ≈ 24.4 pages Version B Mean: 22+22+22+23+23+23+23+24+24+25+26+27 12 ≈ 23.7 pages COMPARATIVE INFERENCE: The mean number of pages read for Versions A and B differ by less than a page. You can infer that Version A and Version B are equally easy to read.

Measures of Center If you have different comparative inferences based on each measure of center, you can draw a conclusion about the situation by looking more closely at the data sets.

Hyacinth Macaw Wingspan Kakapo Wingspan Hyacinth Macaw Weight Weight 30 25 2.8 3.9 37 26 3.7 4.5 39 5.3 41 33 3.0 6.7 45 34 3.1 7.4 48 35 3.4 8.1 52 36 2.9 6.4 57 37.5 3.2 Examples A biology student is studying two species of endangered parrots. One species can fly and the other cannot. Using the data, which species would the student conclude can fly? Explain.

Examples A book publisher is testing two versions of a new book. A random sample of people is given 30 minutes to read each version. Using the data, what might the publisher conclude about the book versions?

HW: Comparing Measures of Center