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Higher Order Thinking Skills: The higher order thinking skills shows examples of questions for this concept at various levels of cognitive demand.

Standard 4.0 Knowledge of Statistics

Topic B. Data Analysis

Indicator 1. Analyze data

Objective b. Interpret box-and-whisker plots

Assessment limit: Use minimum, first (lower) quartile, median (middle quartile), third (upper) quartile, or maximum and whole numbers (0 – 100)

Question

The following box-and-whisker plot represents the average monthly rainfall in millimeters for the Australian Capital Territory (ACT). Source: http://www.about-australia.com/actweat.htm

Average Monthly Rainfall for the ACT (in millimeters)

graph image

Level 1: Knowledge/Comprehension

What are estimates of the median and range for the data set?

Sample correct response: The median of the data set is about 53 millimeters and the range of the data set is about 30 millimeters.

Level 2: Application/Analysis

In the box and whisker plot above: The minimum is 38, the lower quartile is 49, the median is 53.5, the upper quartile is 56.5 and the maximum is 67.

At least what percent of the months have more than 49 millimeters of rainfall?

Sample correct response: Since the lower quartile of the data set is 49, at least 75% of the data is greater than 49 millimeters. Therefore, at least 75% of the 12 months, or 9 months, have more than 49 millimeters of rainfall.

Level 3: Synthesis/Evaluation

A box-and-whisker plot for the Average Monthly Rainfall for the Wetland Region in Equatorial Africa has been drawn below on the same scale as the Average Monthly Rainfall for the Australian Capital Territory (ACT). The lower quartile for the Average Monthly Rainfall for the Wetland Region in Equatorial Africa is 53.5 and its median is 56.5. Compare the amount of average monthly rainfall shown for the Wetland Region in Equatorial Africa to the average monthly rainfall for the ACT in terms of percents or fractions.

Average Monthly Rainfall (in millimeters)

graph image

Sample correct answer:
Although the range of the Average Monthly Rainfall for the Wetland Region in Equatorial Africa is the same as the range for the ACT, 75% of the average monthly rainfall of the Wetland Region in Equatorial Africa is above 56.5, the median of the ACT. The second plot has its lower quartile at the same point of the median of the previous data set, reflecting wetter conditions. 50% of the average monthly rainfall of the Wetland Region in Equatorial Africa is above the upper quartile for the average monthly rainfall for the ACT. This means that half of the data values for the Wetland Region in Equatorial Africa are greater than the upper quartile of the ACT.
/instruction/thinking_skills/mathematics/grade8/xml/4B1b.xml
Resources for Objective 4.B.1.b:
THINKING SKILLS | Sample Assessments |