Box And Whisker Plots And Measures Of Central Tendency Worksheet (Page 2 of 2) in pdf

Box And Whisker Plots And Measures Of Central Tendency Worksheet Page 2

Box and Whisker Plots and Measures of Central Tendency

Answer Key

Notes: When students are making judgements about which measure of central tendency

to use, they need to understand how variability in the data affects the values of the

measures of central tendency. Generally, if you are looking for the best representative

value when there is a skewed set of data, it is better to use the median rather than the

mean. This is because the mean can be influenced by outliers and therefore give a false

idea of the truth.

1 - 2. Students should mention that Data Set I is symmetrical. They can see that the box

and whisker plot is symmetrical whereas the other two plots are not. Data Set II

has half the data that is 10 or less and the other half between 10 and 120, while

Data Set III has half the data falling between 70 and 80 with the other half falling

between 10 and 70. Students should have a solid understanding of median and

how it is represented in a box and whisker plot.

a – b.

Mean

Median

Data Set I

Data Set II

31.25

6.5

58.25

72.5

Data Set III

c. If the data are symmetrical, then the mean and the median are equal. However,

when the data are skewed to the right as in Data Set II, the mean is greater than

the median. When the data are skewed to the left as is the case with Data Set

III, the mean is less than the median. In other words, the mean is pulled in the

direction of the skewedness or outliers while the median is not effected.

If the box and whisker plot is symmetrical, the mean and the median will be the

same. If the data are skewed to the right (you can tell this by a long whisker on

the right side), then the mean will be greater than the median. If the data are

skewed to the left (shown by a long whisker to the left side), then the mean will

be less than the median.

Box And Whisker Plots And Measures Of Central Tendency Worksheet Page 2