2.2-Frequency Distributions and Their Graphs

Question 1

Classes

Answer 1

Intervals of equal width that cover all the values that are observed.

Question 2

Relative Frequency

Answer 2

Relative Frequency = (Frequency / Sum of all Frequencies)

Question 3

Lower Class Limit

Answer 3

The smallest value that can appear in that class.

Question 4

Upper Class Limit

Answer 4

The largest value that can appear in that class.

Question 5

Class Width

Answer 5

The difference between consecutive lower class limits.

Question 6

Requirements for Choosing Classes

Answer 6

• Every observation must fall into one of the classes.
• The classes must not overlap.
• The classes must be of equal width.
• There must be no gaps between classes. Even if there are no observations in a class, it must be included in the frequency distribution.

Question 7

Procedure for Constructing a Frequency Distribution for Quantitative Data

Answer 7

• Step 1: Choose a class width.
• Step 2: Choose a lower class limit for the first class. This should be a convenient number that is slightly less than the minimum data value.
• Step 3: Compute the lower limit for the second class by adding the class width to the lower limit for the first class:
  ​ Lower limit for second class = Lower limit for first class + Class width
• Step 4: Compute the lower limits for each of the remaining classes by adding the class width to the lower limit of the preceding class. Stop when the largest data value is included in a class.
• Step 5: Count the number of observations in each class, and construct the frequency distribution.

Question 8

Histogram

Answer 8

A frequency distribution or a relative frequency distribution put into graphical form.

Question 9

Frequency Histograms

Answer 9

Histograms based on frequency distributions.

Question 10

Relative Frequency Histograms

Answer 10

Histograms based on relative frequency distributions.

Question 11

Guidelines for Selecting the Number of Classes

Answer 11

• For many data sets, the number of classes should be at least 5 but no more than 20.
• For very large data sets, a larger number of classes may be appropriate.

Question 12

Open-Ended

Answer 12

It is sometimes necessary for the first class to have no lower limit or for the last class to have no upper limit. Such a class is called open-ended.

Question 13

Symmetric

Answer 13

A histogram is symmetric if its right half is a mirror image of its left half.

Question 14

Skewed

Answer 14

A histogram is skewed if one side, or tail, is longer than the other.

Question 15

Skewed to the Right

Answer 15

A histogram with a long right-hand tail is said to be skewed to the right, or positively skewed.

Question 16

Positively Skewed

Answer 16

A histogram with a long right-hand tail is said to be skewed to the right, or positively skewed.

Question 17

Skewed to the Left

Answer 17

A histogram with a long left-hand tail is said to be skewed to the left, or negatively skewed.

Question 18

Negatively Skewed

Answer 18

A histogram with a long left-hand tail is said to be skewed to the left, or negatively skewed.

Question 19

Mode

Answer 19

A peak, or high point, of a histogram.

Question 20

Unimodal

Answer 20

A histogram is unimodal if it has only one mode.

Question 21

Bimodal

Answer 21

A histogram that has two clearly distinct modes.

Question 22

Midpoint

Answer 22

The midpoint of a class is the average of its lower class limit and the lower class limit of the next class.

Class Midpoint = (Lower Limit + Lower Limit of next class / 2)