6.2 Estimate for the mean

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 6

Good afternoon!

Schedule: 

• Learning goals
• Estimate for the mean (from grouped data)
• Calculator
• Homework 

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

5

17

2

27

​2​​(n+1)​​=​2​​31​​=15.5th

value. 3rd class will have the 12th up to the 17th values.  Median lies in 50 < w ≤ 60

Grouped frequency tables

a. Find the modal class

b. Find the median class

c. Give an estimate of the range

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

How do you calculate the mean (x̄)?

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             

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

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 

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

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

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? 

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)​​

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)​​

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

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

___________________________

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  = 

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.                                                                                                  

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

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

_________________________     ____

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)

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

Comparing 

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

What is the actual mean? 

x̄ =                               ≈ 37.1

​NumberOfValues​​SumOfValues​​=​19​​705​​

What x̄ do you think is more accurate?

The estimate of x̄

The actual x̄

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”.

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

Take out your diaries/notebooks

Homework for Wednesday 15-3-2023:

                            Practice 2 on p. 332-333 

BRING YOUR FULLY CHARGED CALCULATOR