1. Unit 7. Day 15.

2. How do we determine the mean?
There are three bags, Bag A, Bag B, and Bag C, with 𝟏𝟎𝟎 numbers in each bag. You and your classmates will investigate the population mean (the mean of all 𝟏𝟎𝟎 numbers) in each bag. Each set of numbers has the same range. However, the population means of each set may or may not be the same. We will see who can uncover the mystery of the bags!
How do we determine the mean?

3. Each bag has 100 numbers A B C

4. 𝑌𝑜𝑢𝑟 𝑤𝑖𝑙𝑙 𝑙𝑜𝑜𝑘 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡‼!
Selection 1 2 3 4 5 6 7 8 9 10
Bag A
Bag B
Bag C 9 10 11 14 15 18 19 19 19 20
𝑌𝑜𝑢𝑟 𝑤𝑖𝑙𝑙 𝑙𝑜𝑜𝑘 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡‼!

5. Selection 1 2 3 4 5 6 7 8 9 10
Bag A
Bag B
Bag C 9 10 11 14 15 18 19 19 19 20 8 12 13 13 16 17 17 21 23 23

6. Mean of the Sample of Numbers
Selection 1 2 3 4 5 6 7 8 9 10
Bag A
Bag B
Bag C 9 10 11 14 15 18 19 19 19 20 8 12 13 13 16 17 17 21 23 23 2 2 4 5 9 12 14 16 19 19
Mean of the Sample of Numbers
Bag A
Bag B
Bag C
#2:𝑀𝑒𝑎𝑛 𝐴 −𝑀𝑒𝑎𝑛 𝐵
#3:𝑀𝑒𝑎𝑛 𝐴 −𝑀𝑒𝑎𝑛 𝐶

7. Mean of the Sample of Numbers
Calculate the Means
Mean of the Sample of Numbers
Bag A
Bag B
Bag C
15.4
16.3
10.2
Are the sample means you calculated the same as the sample means of other members of your class? Why or why not?
Fancy math word:
Sampling Variability

8. Mean of the Sample of Numbers
Calculate the Means
Mean of the Sample of Numbers
Bag A
Bag B
Bag C
15.4
16.3
10.2
My sample B is larger than my sample A. Is this true for you too?
My sample C is smaller than my sample A and B. Is this true for you too? :

9. Let’s make three class dot plots!
Bag A
Bag B
Bag C

10. Q: Based on the class dot plots of the sample means, do you think the mean of the numbers in Bag A and the mean of the numbers in Bag B are different?
Q: Do you think the mean of the numbers in Bag A and the mean of the numbers in Bag C are different?

11. Mean of the Sample of Numbers
Mean of the Sample of Numbers
Bag A
15.4
Bag B
16.3
Bag C
10.2 
Mean A – Mean B:
15.4−16.3 =
−0.9
15.4−10.2 =
5.2
Mean A – Mean C:

12. Let’s make two class dot plots!
Mean A – Mean B:
Mean A – Mean C:
How do the centers of the class dot plots for
(Mean A – Mean B) and (Mean A – Mean C) compare?

13. The numbers inside Bag A are the SAME as the numbers in Bag B!!!!!!!
Guess what? B A C
The numbers inside Bag A are the SAME as the numbers in Bag B!!!!!!!
So why wasn’t Mean A−Mean B always 0?
“Sampling Variability”
Each bag has a population mean that is either 10.5 or What do you think the population mean is for each bag?

14. Did you learn what you should’ve?
“This lesson showed that when taking samples from the same population, the mean of each sample will most likely not be the same, which is called sampling variability”
“Students understand that a meaningful difference between two sample means is one that is greater than would have been expected due to just sampling variability.”