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

VOCABULARY 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). We already know how to find Q2 because it is the median. Q3 and Q1 are found in a very similar manner.

VOCABULARY (and, how do we find it?) REWIND / REMIND: To locate the median (Q2), we found the central value(s) of the data. In the data set below, the median, Q2, is 17. Data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. 50% 50% The median (Q2), divides the data in half so that 50% is below (lower than) the median and 50% is above (higher than) the median.

VOCABULARY (and, what does that mean?) Q3 does the same thing (as the median) for the higher half (upper) of the data, cutting the higher 50% (approximate) into two approximately 25% pieces. Q3 25% 25% Data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. 50% 50% Median (Q2)

VOCABULARY (and, what does that mean?) And, Q1 does the same thing (as the median) for the lower half of the data, cutting the lower 50% (approximate) into two approximately 25% pieces. Q1 25% 25% Data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. 50% 50% Median (Q2)

VOCABULARY (and, what does that mean?) Together, Q1, Q2 (median), and Q3 separate the data into four sections of (approximately) 25% of the data. Q1 Q2 Q3 25% 25% 25% 25% Data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. 50% 50% Median (Q2)

VOCABULARY (or, what does that mean?) 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. 75% 25% In the data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }, Q3 is 23. Q3

VOCABULARY (or, what does that mean?) 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. 25% 75% In the data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }, Q1 is 8. Q1

VOCABULARY (and, how do we find it?) IT IS IMPORTANT, to keep in mind, the median IS NEVER INCLUDED, when locating Q3 or Q1. Q1 Q3 Data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. Median (Q2) 14.5 Data set: { 2, 9, 10, 12, 14, 15, 16, 22, 25, 28 }. Q1 Q3

VOCABULARY (or, how do we find it?) INTER-QUARTILE RANGE (IQR): The IQR is the range from Q3 to Q1. It is calculated simply by subtracting Q1 from Q3: Q3 – Q1 = IQR. In the data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }, Q3 = 23, Q1 = 8. Q1 Q3 Q3 – Q1 = IQR 23 – 8 = 15 IQR = 15 .

VOCABULARY (or, what does that mean?) Since the Inter-Quartile Range (IQR) is the difference between Q3 and Q1, the IQR (approximately) represents the central (or middle) 50% of the data. 25% 50% 25% In the data set: { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 }. Q1 Q3 Q1 = 8, IQR = 15, Q3 = 23.

VOCABULARY WORDS QUARTILE FIRST QUARTILE (Q1) SECOND QUARTILE (Q2 / MEDIAN) THIRD QUARTILE (Q3) INTER-QUARTILE RANGE (IQR)

: CLASSWORK TO TURN IN 1. { 4, 5, 8, 9, 17, 17, 17, 21, 23, 25, 27 } ASSIGNMENT 07 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 }