Notes 2.1 (Part 1)

Frequency distribution and their graphs

What you should learn

• 1. How to construct a frequency distribution including limits, boundaries, midpoints, relative frequencies and cumulative frequencies.

• 2. How to construct frequency histograms, frequency polygons, relative frequency histograms and ogives.

Frequency Distributions• Frequency distribution: is a table that shows classes

(or intervals) of data entries, with a count for each class.

f : frequency (or how many times it occurs for a particular class)

• Each class will have a lower class limit and an upper class limit.

• Lower Class Limits: 45,50,55,60,65,70…• Upper Class Limits: 49,54,59,64,69,74…

Class width: the distance between the lower (or upper) class limits of consecutive classes

54 – 49 = 550 – 45 = 570 – 65 = 594 – 89 = 5

Class width is 5.You only have to do it one time.

Constructing a frequency

1. Decide on the number of classes that you want to include in your frequency distribution. (Should have between five and 20 classes)

2. Find the class width CW = Max Entry – Min Entry number of classes

(Always round up to the next whole number)

3. Find the class limits. Use min entry as lower class limit (LCL) of first class. Find the remaining LCL by adding the class with to each preceding class. Then find upper class limits.

4. Make a tally mark for each data entry in the row of the appropriate class.

5. Count the tally marks to find the total frequency ( f ) for each class.

Step to solving

• 1. State the number of classes• 2. Find the min and max values and the

class width.• 3. Find the class limits.• 4. Tally the data entries.• 5. Write the frequency f for each class.

Warm Up: Try it yourself 1• Construct a frequency distribution using the ages of

Akhiok , Alaska given below. Use six classes.

• 28, 6, 17, 48, 63, 47, 27, 21, 3, 7, 12, 39, 50, 54, 33, 45, 15, 24, 1, 7, 36, 53, 46, 27, 5, 10, 32, 50, 52, 11, 42, 22, 3, 17, 34, 56, 25, 2, 30, 10, 33, 1, 49, 13, 16, 8, 31, 21, 6, 9, 2, 11, 32, 25, 0, 55, 23, 41, 29, 4, 51, 4, 6, 31, 5, 5, 11, 4, 10, 26, 12, 6, 16, 8, 2, 4, 28

Assignment #12

• Construct the frequency distribution table for the following. (class, tally and f )

• 1. Number of rainy days in Seattle, WA during the last 15 years. (5 classes)

• 175, 152, 105, 201, 138, 111, 117, 142, 193, 101, 123, 114, 164, 150, 184

• 2. Number of victories in the last 22 years by the Oakland Raiders. (6 classes)

• 8, 5, 5, 4, 2, 4, 5, 4, 11, 10, 12, 8, 8, 4, 7, 8, 9 10, 7, 9, 12, 8

Warm Up

• Construct a frequency distribution chart with 5 classes. The number of jobs a person has had before their 40th birthday.

• 2, 15, 6, 8 , 9, 10, 1, 8

• Need class, tally and frequency (if you can get midpoints and class boundaries).

Notes 2.1 (Part 2)

Midpoint, Class Boundaries, Relative Frequency and Cumulative

Frequency

Midpoint• For each class you add the LCL and UCL and

divide by 2, this gives you the midpoint for each class.

• 45 + 49 = 47 2

Class Boundaries

• In order to obtain the class boundaries you subtract .5 from all the LCL and add .5 to all UCL.

Relative Frequency

• Take the class of each frequency and divide it by the ∑ f .

Cumulative Frequency

• You keep a running count of the frequencies.

Notes 2.1 (Part 3)

Graphing

Warm-Up

• Number of accidents during the past 12 months at the Bristol and First Street intersection. (5 classes)

• 14, 20, 18, 34, 17, 24, 45, 52, 37, 29 , 21, 22

• Frequency Histogram: (example on page 36)– Bar graph– Bars much touch– Frequency goes on left side– You can use either midpoints or class boundaries

• Frequency polygon (example on page 37)– Line graph– Looks like a mountain– Must use midpoints– You add an extra midpoint to front and back of

graph– Frequency goes on left

• Relative Frequency Histogram– Bar graph– Bars must be touching– Must use class boundaries on the bottom– Relative frequency goes on the left side of graph

• Ogive: (Example on page 39)– Line graph– Looks like your going uphill– Must use class boundaries on the bottom of graph– Must use cumulative frequency on the left hand

side of graph.– The lower class limit of the first class must start at

zero.