# 6.2 Estimate for the mean

Good afternoon!
Schedule:
• Learning goals
• Estimate for the mean (from grouped data)
• Calculator
• Homework
1 / 28
Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 6

In deze les zitten 28 slides, met interactieve quizzen en tekstslides.

## Onderdelen in deze les

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

#### Slide 1 -Tekstslide

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 3 -Tekstslide

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 -Tekstslide

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

#### Slide 5 -Tekstslide

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 -Tekstslide

How do you calculate the mean (x̄)?

#### Slide 7 -Woordweb

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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

#### Slide 20 -Open vraag

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

What x̄ do you think is more accurate?

The estimate of x̄
The actual x̄

#### Slide 25 -Poll

Calculator
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 -Tekstslide

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