6.2 Estimate for the mean

Good afternoon!
Schedule: 
  • Learning goals
  • Estimate for the mean (from grouped data)
  • Calculator
  • Homework 
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Good afternoon!
Schedule: 
  • Learning goals
  • Estimate for the mean (from grouped data)
  • Calculator
  • Homework 

Slide 1 - Diapositive

Learning goals 
At the end of this lessons I can:
  • Calculate the estimate for the mean from grouped data 
  • Calculate the estimate for the mean on my Ti-NSpire

Slide 2 - Diapositive

Slide 3 - Diapositive

5
17
2
27
2(n+1)=231=15.5th
value. 3rd class will have the 12th up to the 17th values.  Median lies in 50 < w ≤ 60

Slide 4 - Diapositive

Grouped frequency tables
a. Find the modal class
b. Find the median class
c. Give an estimate of the range

Slide 5 - Diapositive

Grouped frequency tables
a. Modal class             70 ≤ s < 80                 
b. Find the median class         80 ≤ s <100
c. Give an estimate of the range     Range estimate = 130 - 60 = 70
Cumulative frequency 
8
23
35
45
53
56
60

Slide 6 - Diapositive

How do you calculate the mean (x̄)?

Slide 7 - Carte mentale

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

We guess!
          we make an estimation             

Slide 8 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

- Assume that all the data in each class interval has the value of the upperclass boundary. 
Calculate the mean

Slide 9 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

- Assume that all the data in each class interval has the value of the upperclass boundary. 
Calculate the mean

Upperbound mean = 2.92 pets 

Slide 10 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

- Assume that all the data in each class interval has the value of the Lowerclass boundary. 
Calculate the mean


Slide 11 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

- Assume that all the data in each class interval has the value of the Lowerclass boundary. 
Calculate the mean

Lowerbound mean = 0.92 pets

Slide 12 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1
How can we calculate x̄ (mean) if we don't know the values? 

Upperbound mean = 2.92 pets 

Lowerbound mean = 0.92 pets

What value would be better to represent all data in a class interval? 

Slide 13 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1

Take the Midpoint of every class

Midpoint =         
2(classmaximum+classminimum)

Slide 14 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
Midpoint
0 < x ≤ 2
8
2 < x ≤ 4
4
4 < x ≤ 6
1







Midpoint =         
2(classmaximum+classminimum)

Slide 15 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
Midpoint
Midpoint · Frequency
0 < x ≤ 2
8
1
2 < x ≤ 4
4
3
4 < x ≤ 6
1
5

Slide 16 - Diapositive

Estimate for the mean
# of pets, x 
Frequency
Midpoint
Midpoint · Frequency
0 < x ≤ 2
8
1
8
2 < x ≤ 4
4
3
12
4 < x ≤ 6
1
5
5
Estimate for x̄ =  
Sum of (midpoint  · frequency)
             Number of values

___________________________

Slide 17 - Diapositive

Estimate for x̄ (mean)
# of pets, x 
Frequency
Midpoint
Midpoint · Frequency
0 < x ≤ 2
8
1
8
2 < x ≤ 4
4
3
12
4 < x ≤ 6
1
5
5
Estimate for x̄  = 

Slide 18 - Diapositive

How to find an estimate for the mean
1. Calculate the Midpoint of every class
2. Calculate Midpoint · Frequency
3. Calculate the sum of Midpoint · Frequency
4. Calculate the number of values

5.                                                                                                  

Slide 19 - Diapositive

Copy this table and calculate and estimate for x̄ (mean).

Slide 20 - Question ouverte

Time spend, x, (min)
Frequency
Midpoint
Midpoint · Frequency
5 < x ≤ 20
7
12.5
87.5
20 < x ≤ 35
4
27.5
110
35 < x ≤ 50
2
42.5
85
50 < x ≤ 65
5
57.5
287.5
65 < x ≤ 80
0
72.5
0
80 < x ≤ 95
1
87.5
87.5
                                                87.5 + 110 + 85 + 287.5 + 0 + 87.5       657.5
Estimate for x̄ (mean)  =               7 + 4 + 2 + 5 + 0 + 1              =     19   ≈ 34.6 min
_________________________     ____

Slide 21 - Diapositive

Frequency Tables
Time spend, x, (min)
Frequency
Midpoint
Midpoint · Frequency
5 < x ≤ 20
7
12.5
87.5
20 < x ≤ 35
4
27.5
110
35 < x ≤ 50
2
42.5
85
50 < x ≤ 65
5
57.5
287.5
65 < x ≤ 80
0
72.5
0
80 < x ≤ 95
1
87.5
87.5
Time spent on Math Homework (MP4 2022)

Slide 22 - Diapositive

Comparing 
An estimate of x̄ was 34.6 min spent on Math homework (per day). 

What is the actual mean

Calculate the mean time spent on Math homework! 
n = 19

Slide 23 - Diapositive

Comparing 
An estimate of x̄ was 34.6 min spent on Math homework (per day). 

What is the actual mean

x̄ =                               ≈ 37.1
NumberOfValuesSumOfValues=19705

Slide 24 - Diapositive

What x̄ do you think is more accurate?

The estimate of x̄
The actual x̄

Slide 25 - Sondage

Calculator
1. Open a “List & Spreadsheet” in your documents.
2. Input Mid-interval value into column A, and title it “midv”.
3. Input the Frequency into column B, and title it “freq”.
4. Press “menu”, select 4: Statistics, 1: Stat Calculations, & 1: One-Variable Statistics.
5. Choose 1 as your number of lists, “mid” as your X1 List, and “freq” as your Frequency List.
6. Enter all the way until you get to “OK”.

Slide 26 - Diapositive

Estimate of x̄ on the calculator
Check the Estimate for the mean amount of pets with your calculator
# of pets, x 
Frequency
Midpoint
Midpoint · Frequency
0 < x ≤ 2
8
1
8
2 < x ≤ 4
4
3
12
4 < x ≤ 6
1
5
5

Slide 27 - Diapositive

Take out your diaries/notebooks


Homework for Wednesday 15-3-2023:
                            Practice 2 on p. 332-333 

BRING YOUR FULLY CHARGED CALCULATOR


Slide 28 - Diapositive