Download Lesson 6 Mar IV

Math Tech IIII, Mar 6
Grouped Data Computations
Book Sections: 2.3
Essential Questions: How do I compute and use statistical values? How
do I computed statistical values from non-traditional data types?
What is grouped data?
Standards: PS.SPID.2, .3
Grouped Data
• Grouped data – data that is summarized in a frequency
table
• Tabular only – no raw data is known
• We use what we know – class width and frequency – to
compute statistics
• Mean
• Standard deviation
• These computations are approximate values
Finding the Mean of a Group
___
X
 f  Xm

n
Where f is the class frequency, Xm is
the midpoint, and n is the total
frequency.
Finding the Standard Deviation of a Group
We would fight the this battle via variance, like last time

2

f

X
m   f  X m  / n
2
s 
n 1
2

Where f is the class frequency, Xm is
the midpoint, and n is the total
frequency and Xm2 is the square of
the midpoint.
What It Looks Like
Class (interval)
5.5-10.5
10.5-15.5
15.5-20.5
20.5-25.5
25.5-30.5
30.5-35.5
35.5-40.5
Frequency (f)
1
2
3
5
4
3
2
Definition
Class (interval)
5.5-10.5
10.5-15.5
15.5-20.5
20.5-25.5
25.5-30.5
30.5-35.5
35.5-40.5
Frequency (f)
1
2
3
5
4
3
2
Definition: Modal
Class – The class
with the greatest
frequency
Two List Computations
On Your Calculator
• There are times when we have to use the 1-Var Stats
computation using two lists. Those are:
 Grouped data computations
 Weighted Mean computations
 Probability Distribution computations
• The format is 1-Var Stats L1,L2
 You must specify the lists you want the calculator to use
• The prompting calculator will prompt for the two lists
List: L1
FreqList: L2
Calculate
Grouped Data Class Width
• We use the class midpoint as the value of the class in any
grouped statistical computation.
• The midpoint formula: midpo int 
(classlow  class high)
2
where classlow and classhigh are the class boundries
Finding the Mid-Point
midpo int 
Class (interval)
5.5-10.5
10.5-15.5
15.5-20.5
20.5-25.5
25.5-30.5
30.5-35.5
35.5-40.5
Frequency (f)
1
2
3
5
4
3
2
(classlow  class high)
2
Making it Work
Add three more columns to the table, as shown
Class (interval)
5.5-10.5
10.5-15.5
15.5-20.5
20.5-25.5
25.5-30.5
30.5-35.5
35.5-40.5
Frequency (f)
1
2
3
5
4
3
2
Making it Work
Add two more columns to the table, as shown
Class (interval)
Frequency (f)
5.5-10.5
10.5-15.5
15.5-20.5
20.5-25.5
25.5-30.5
30.5-35.5
35.5-40.5
1
2
3
5
4
3
2
n = 20
MidPoint (Xm) f ·Xm
f ·Xm2
Help Me Mr Texas!
• Lucky you, the calculator can do it!
Calculator needs – midpoints in L1 and frequencies in L2
Calculator Setup
• You must use two lists to accomplish this calculator
computation
1. Start with [STAT]  select {EDIT}
2. Put class midpoints into L1: (lo + hi)/2
3. Put frequencies into L2: one per midpoint
4.
Press [STAT]  select {CALC}, 1-Var stats L1,L2
• Only use mean and standard deviation
Example
Identify the modal class and compute the mean and standard
deviation of this frequency table:
Class (interval)
2.1-2.7
2.8-3.4
3.5-4.1
4.2-4.8
4.9-5.5
5.6-6.2
Frequency (f)
12
13
7
5
2
1
Big Example
Identify the modal class and compute the mean and standard
deviation of this distribution:
Class (interval)
0-4
5-9
10-14
15-19
20-24
25-29
Frequency (f)
140
153
207
187
168
145
What If?
The class is a number and not an interval?
Identify the modal class and compute the mean and standard
deviation of this distribution:
Class
Frequency (f)
1
1
2
8
3
3
4
5
5
4
6
3
7
7
Class work: CW 3/6/17, 1-10
Homework: None