1. Statistics Notes 01/09/2017 Notes on explicitly writing out data
Center-range vs. Min-Max

2. Data Expansion Data/Frequency Range/Frequency
If you have Data/Frequency, you can expand the data
10,10,10,11,11,12,12
Find Mean, Median, Mode using the table or the expanded data
If you have Range and frequency you cannot expand the data
Cannot expand – must use graph to find Q1,Q2,Q3,Q3.
Data
Frequency 10 3 11 2 12
Data
Frequency
10≤𝑥<11 3
11≤𝑥<12
12≤𝑥<13 2

3. And now for something completely different
Center and radius
Writing to Center and Radius
𝑥=10±2
Then x can be written as
10−2 ≤𝑥≤ 10+2
So equation for
𝑥=𝐶±𝑅
𝐶−𝑅 ≤𝑥≤(𝐶+𝑅)
14≤𝑥≤18
Center=average
𝐶= = 32 2 =16
𝑅= 18−14 2 = 4 2 =2
𝐶= 𝑀𝑎𝑥+𝑀𝑖𝑛 2
𝑅= 𝑀𝑎𝑥−𝑀𝑖𝑛 2

4. “Center” and “Range” If 𝑥=5±2→3≤𝑥≤7 If 𝑥=7±3→ If 𝑥=50±5→ If 𝑥=25±7→

5. Sample Problems
A math test was given to a class. The scores were 72±16 points. What is the range of the scores?
The weight of 80 chocolate bars in a batch is 120±22 grams. What is the range of the weights?
The time it takes to build a 3 story office building is between 350 and 410 days. Write this in Center-Radius format.
Rabbits have a litter between Write in center radius format

6. Measure of Center and Dispersion
Median
Mean
Center: Median
Dispersion
IQR (Q3-Q1)
5 point summary (min-Q1- Median-Q3-Max)
Center – Mean (average)
Dispersion – Standard Deviation. The standard deviation is like the radius.
It is different in that it only accounts for 2/3 (66%) of the data.
Rule

7. Standard Deviation
Formula 𝜎= ∑ 𝑥−𝜇 2 𝑁 It is like the average of distance to the mean
It makes most sense of your data are in a normal distribution (also called a Bell Curve). But due to a theorem called “Central Limit Theorem”, many important parameters are in a Bell Curve.
The Rule.
Standard Deviation from mean
Amount of Data
Graph 1
67% 2
95% 3
99%

8. Practice Find the mean and standard deviation of the following
By hand : 3,3,4,5,6,7,8
By Calculator: 12,13,14,14,15,16,17,17,19
By hand then by calculator
Data
Frequency 1 2 3 4