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

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.

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.

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.

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).

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.

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.

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.

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;

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: 4 1.5 = 6 UPPER INTER-QUARTILE LIMIT (U - IQL): 17 2. Q3 + IQL: 11 + 6 = 17 LOWER INTER-QUARTILE LIMIT (L - IQL): 1 3. Q1 - IQL: 7 - 6 = 1

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.

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

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

: 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 }