1. Unit 2: Descriptive Statistics
Part Three
Making the calculations
and the language we speak

2. REVIEW
OBSERVATIONS: The number of data points in a category or data set is referred to as the number of observations, or simply as observations.
FREQUENCY: The frequency is the number of times a specific data value occurs in a data set.

3. REVIEW DATA SET: A data set is any collection of data points.
UNORDERED (data set): Any collection of data points in which the observations are not arranged in a logical and determined order by category, but in the order they were observed.
ORDERED (data set ): Any collection of data points in which the observations are arranged in a logical and determined order, usually to a single category.

4. REVIEW
RANGE: The difference or distance between the two most extreme data points.
MEAN: The mean is the arithmetic average of any set of numbers.
MODE: The mode is the data value that appears most often. There can be one mode, more than one mode, or no mode.

5. REVIEW
MEDIAN: The median is the central number, center number, or central figure of any ordered set of numbers. Medians can be a single number in the data set, or an average of the two central figures.
QUARTILE: A quartile is 25% of a data set. Quartile means one-quarter, or 25%. There are three quartiles, the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3).

6. REVIEW
Q3 / QUARTILE 03 / THIRD QUARTILE: Q3 is the point in any data set in which approximately 25% of the data is above Q3 and approximately 75% of the data is below Q3.
Q1 / QUARTILE 01 / FIRST QUARTILE: Q1 is the point in any data set in which approximately 75% of the data is above Q1 and approximately 25% of the data is below Q1.

7. REVIEW
INTER-QUARTILE RANGE (IQR): The IQR is the range between Q3 to Q1. It is calculated by subtracting Q1 from Q3: Q3 – Q1 = IQR.
The Inter-Quartile Range (IQR) represents the central (or middle) 50% of the data.

8. VOCABULARY (What is it, and how do I find it?)
NEW
INTER-QUARTILE LIMIT (IQL): The Inter-quartile limit is the area in which data is normal to the data set. Any data points that fall outside of the IQL are outliers.
UPPER INTER-QUARTILE LIMIT (U-IQL): The upper inter-quartile limit is the point (limit) beyond which any (higher) remaining data points are outliers.
LOWER INTER-QUARTILE LIMIT (L-IQL): The lower inter-quartile limit is the point (limit) beyond which any (lower) remaining data points are outliers.

9. VOCABULARY (What is it, and how do I find it?)
INTER-QUARTILE LIMIT (IQL): The Inter-quartile limit is the area in which data is normal to the data set. Any data points that fall outside of the IQL are outliers.
Determining the IQL is a three-step process:
1. IQL: Multiply the IQR by 1.5;
2. U-IQL: Add the IQL to Q3 to determine the upper
inter-quartile limit;
3. L-IQL: Subtract the IQL from Q1 to determine the
lower inter-quartile limit;

10. VOCABULARY (What is it, and how do I find it?)
INTER-QUARTILE LIMIT (IQL): HOW?
Determining the IQL:
1. Multiply the IQR by 1.5; Q1
Median Q3
Outlier
2. Add the IQL to Q3 to
determine the upper limit;
3. Subtract the IQL from Q1 to
determine the lower limit;
SET = { 1, 5, 7, 7, 8, 9, 9, 10, 11, 13, 19 } 1 17
IQR: 11 – 7 = 4
L - IQL
U - IQL
1. IQL: = 6
UPPER INTER-QUARTILE LIMIT (U - IQL): 17
2. Q3 + IQL: = 17
LOWER INTER-QUARTILE LIMIT (L - IQL): 1
3. Q1 - IQL: = 1

11. VOCABULARY (What is it, and how do I find it?)
OUTLIER: An outlier is any data point that lies outside of the upper or lower inter-quartile limit.
MAXIMUM (MAX): The maximum of a data set is the highest value data point within the Inter-quartile limit.
MINIMUM (MIN): The minimum of a data set is the lowest value data point within the Inter-quartile limit.

12. VOCABULARY (What is it, and how do I find it?)Q1
Median Q3
Outlier
Max: 13
Min
Max
SET = { 1, 5, 7, 7, 8, 9, 9, 10, 11, 13, 19 }
Min: 1 1 17
IQR: 11 – 7 = 4
L - IQL
U - IQL

13. VOCABULARY WORDS NEW INTER-QUARTILE LIMIT (IQL)
UPPER INTER-QUARTILE LIMIT (U-IQL)
LOWER INTER-QUARTILE LIMIT (L-IQL)
OUTLIER
MAXIMUM (MAX)
MINIMUM (MIN)

14. : CLASSWORK TO TURN IN 1. { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }
ASSIGNMENT 09
CLASSWORK TO TURN IN :
FIND THE (OBSERVATIONAL) FREQUENCY, RANGE, MEAN, MEDIAN, AND MODE OF THE FOLLOWING DATA SETS:
1. { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }
2. { 1, 5, 7, 10, 12, 14, 15, 16, 22, 25, 25, 30 }
3. { 2, 9, 10, 12, 14, 15, 16, 22, 25, 28 }
4. { 2, 5, 9, 13, 15, 16, 16, 20, 24, 28, 32, 37 }
5. { -5, -2, 0, 2, 4, 5, 6 }
6. { 36, 40, 42, 44, 44, 46, 48, 48, 50 }
7. { 2, 4, 9, 12, 13, 14, 15, 16, 19, 24, 26 }