Transcript Finding the Class Limits

Intro Stats
Lesson 2.1 A
Objective: SSBAT construct a frequency distribution.
Standards: S2.5B
A Limited Lunch
At lunch, twelve of the children chose from the following
types of sandwiches: peanut butter, jelly, peanut butter and
jelly, marshmallow fluff, jelly and fluff, or peanut butter
and fluff. Oliver does not like nuts and so chose to have
just a jelly sandwich, as did Kenny. Kate had plain peanut
butter on her sandwich and so did David because he
doesn’t like jelly or marshmallow fluff. A sandwich with
marshmallow fluff only was taken by Mariko, while Kristen
chose one with marshmallow fluff and peanut butter. Sam
and Stephanie wanted a sandwich with peanut butter and
jelly as did Laura and Isabel and a jelly and fluff sandwich
was chosen by both Ty and Brandon.
Peanut
Peanut
Butter
Butter and
Jelly
Jelly and
Fluff
Fluff
Peanut
Butter and
Jelly
Fluff
David
Laura
Kenny
Brandon
Kate
Sam
Oliver
Ty
Mariko
Kristen
Stephanie
Isabel
The same information as the paragraph is shown in the
table – which is easier to understand?
Frequency Distribution
 A table that shows Classes/Intervals of data
entries with a count of the number of entries in
each class.
Frequency (f)
 The number of data entries in a class
Example of a Frequency Distribution
Class
Frequency, f
1–5
5
6 – 10
8
11 – 15
6
16 – 20
8
21 – 25
5
26 – 30
4
Lower Class Limit
 The smallest number that can belong to a class
Upper Class Limit
 The largest number that can belong to a class
Class Width
 The difference between consecutive Lower (or
upper) limits in a class
Class
Frequency, f
1–5
5
6 – 10
8
11 – 15
6
16 – 20
8
21 – 25
5
26 – 30
4
Examples:
1. What are the Lower Class Limits?
 1, 6, 11, 16, 21, 26
2. What are the Upper Class Limits?
 5, 10, 15, 20, 25, 30
Class
Frequency, f
1–5
5
6 – 10
8
11 – 15
6
16 – 20
8
21 – 25
5
26 – 30
4
Examples:
3. What is the class width?
 6–1 =
5
Range of the Data
 The difference between the Highest number
and the Lowest number in the Data set
 Biggest # minus Smallest #
 Maximum – Minimum
Constructing a Frequency Distribution
1. Decide on the number of Classes to use
 Should be between 5 and 20
2. Find the class width
3. Find the Class Limits
4. Make a tally mark for each data entry in the row
5. Count the tally marks to find the total frequency, f,
for each class
Finding the class width
1. Determine the range of the data
2. Divide the range by the number of classes
3. Always go UP to the next whole number (even if it is a whole number to begin with)
Finding the Class Limits
1. Use the smallest data entry as the Lower Limit of
the 1st class.
2. To find the other Lower Limits, Add the class width
to the previous lower limit. Continue doing this
until you have all the lower limits.
3. Then find the Upper Limit of the first class, using
the lower limits to guide you. Remember classes
cannot overlap. Find the other upper limits in a
similar manner.
1. The number of text messages received in one
hour by 26 different students are listed below.
Create a Frequency Table that has 5 classes.
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
First: Find the Maximum and Minimum data entry
 1 and 29
Second: Find the Range using these 2 entries
 29 – 1 = 28
Continued:
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
Third: Find the class width (the problem asks for 5 classes)
28 ÷ 5
= 5.6 Round to 6
The class width is 6
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
4th: Find the Lower Limits (class width is 6)
The first lower limit is
1
(Now add 6 to this number to get the next one)
1
7
13
19
25
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
 Make table and put lower limits in it (keep in mind the problem
asked for 5 classes – so you will need 5 rows.
Class
1–
7–
13 –
19 –
25 –
Tally
Frequency
(f)
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
 Find the upper class limits by going 1 less than the next lower
limit. Then Add the class width to 24 to get the last upper class
Class
1–6
7 – 12
13 – 18
19 – 24
25 – 30
Tally
Frequency
(f)
2, 8, 10, 11, 16, 16, 25, 29, 1, 8, 12, 19, 20,
22, 29, 5, 7, 12, 17, 21, 26, 3, 9, 12, 17, 20
 Using the numbers from the data set, put tallies in the
appropriate row of the table and then add to get the Frequency
Class
1–6
7 – 12
13 – 18
19 – 24
25 – 30
Tally
llll
lllll llll
llll
lllll
llll
Frequency
(f)
4
9
4
5
4
2. The number of minutes 30 internet subscribers
spent on the internet during their most recent
session are listed below.
Create a Frequency Table that has 7 classes.
50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54,
42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33
First: Find the Maximum and Minimum data entry
 7 and 86
Second: Find the Range using these 2 entries
 86 – 7 = 79
50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54,
42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33
Third: Find the class width.
79 ÷ 7 = 11.29 Round to 12
The class width is 12
Fourth: Find all the lower limits – You need 7 classes
7
19
31
43
55
67
79
50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54,
42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33
 Make table and put lower limits in it
 Find the upper class limits by going 1 less than the next lower limit.
Then add the class width to 78 to get the last upper limit
Class
7 – 18
19 – 30
31 – 42
43 – 54
55 – 66
67 – 78
79 – 90
Tally
Frequency
(f)
50, 40, 41, 17, 11, 7, 22, 44, 28, 21, 19, 23, 37, 51, 54,
42, 86, 41, 78, 56, 72, 56, 17, 7, 69, 30, 80, 56, 29, 33
 Using the numbers from the data set, put tallies in the
appropriate row of the table and then add to get the Frequency
Class
7 – 18
Tally
Frequency
(f)
XXXXX
5
19 – 30
XXXXXXX
7
31 – 42
XXXXXX
6
43 – 54
XXXX
4
55 – 66
XXX
3
67 – 78
XXX
3
79 – 90
XX
2
∑f
 Means the sum of all the Frequencies
 To find this number, add all of the numbers in
the frequency column together
 ∑ is Greek for “sum of”
 The sum of the frequencies (∑ f) should
Equal the number of data entries in the
beginning problem
Class
7 – 18
Tally
Frequency
(f)
XXXXX
5
19 – 30
XXXXXXX
7
31 – 42
XXXXXX
6
43 – 54
XXXX
4
55 – 66
XXX
3
67 – 78
XXX
3
79 – 90
XX
2
∑ f = 30
Homework
Worksheet 2.1 A