Chapter 7: Summarizing and Displaying Measurement Data

Question 1

average/ mean

Answer 1

central measure helpful for data sets without significant outliers

Question 2

median

Answer 2

central measure that shows the value in the physical center of the data

Question 3

mode

Answer 3

central measure that shows the most common value on the list

Question 4

outliers

Answer 4

scores far removed from the rest of the data; in a boxplot, an outlier is defined to be any value that is more than 1.5 IQR beyond the closest quartile.

Question 5

variability

Answer 5

the degree to which the values in a set of data are spread out

Question 6

range

Answer 6

measure of variability that computes the difference between the maximum and minimum

Question 7

shape

Answer 7

when data is represented in a grab, shape allows us to see where values tend to be clumped

Question 8

stemplot/ stem-and-leaf plots/ stem-and-leaf diagrams

Answer 8

note that these stems should have equally spaced intervals

Question 9

truncate

Answer 9

to truncate a number, simply drop off the unused digits

Question 10

histograms

Answer 10

are pictures related to stemplots. For very large data sets, a histogram is more feasible than a stemplot because it doesn’t list every data value.

To create a histogram, divide the range of the data into intervals in much the same way as we did when creating a stemplot. But instead of listing each individual value, simply count how many fall into each part of the range. Draw a bar whose height is equal to the count for each part of the range. Or, equivalently, make the height equal to the proportion of the total count that falls in that interval.

Question 11

symmetric data

Answer 11

a data set in which, if you were to draw a line through the center, the picture on one side would be a mirror image of the picture on the other side.

Question 12

bell-shaped data set/ bell curve

Answer 12

in which the picture is not only symmetric but also shaped like a bell.

Question 13

unimodal

Answer 13

used to describe a data set there is a single
prominent peak in a histogram or stemplot

Question 14

bimodal

Answer 14

If there are two prominent peaks, the shape is called bimodal, meaning “two modes.”

Question 15

skewed

Answer 15

a data set that is basically unimodal but is substantially off from being bell-shaped.

Question 16

skewed to the left

Answer 16

the higher values are more spread out
than the lower values; the lower values are more clumped

Question 17

skewed to the right

Answer 17

the lower values are more spread out and the higher ones tend to be clumped.

Question 18

five number summary

Answer 18

is a useful way to summarize a long list of numbers. As the name implies, this is a set of five numbers that provide a good summary of the entire list. There numbers are: the mean, the 1st quartile, the 2nd quartile, the maximum, and the minimum.

Question 19

lower quartile

Answer 19

The quartiles are simply the medians of the two halves of the ordered list. The lower quartile—because it’s halfway into the first half—is one quarter of the way from the bottom.

Question 20

upper quartile

Answer 20

The quartiles are simply the medians of the two halves of the ordered list. Similarly, the upper quartile is one quarter of the way down from the top.

Question 21

boxplot/ box-and-whisker plot

Answer 21

A visually appealing and useful way to present a five-number summary.

1. Draw a horizontal number line with the maximum and minimum.
2. Draw a retangle dictating the upper quartiles, lower quartiles, and median.
3. Calculate interquartile range
4. Multiply by 1.5 & draw whiskers from the box the length of the the product
5. Use asterisks to notate outliers

Question 22

interquartile range

Answer 22

distance/ difference between the upper and lower quartiles