Unit 2 Section 2.5

2.5: Measures of Position Measures of position are used to locate the position of a data value within a data set. Measures of Position Standard Score (z score) Percentiles Deciles Quartiles

Section 2.5 Quartiles– divide the data set into 4 equal groups. The quartiles are separated by the values Q1, Q2, and Q3. Q1 – About 25% of the data falls below this value Q2 – About 50% of the data falls below this value Q3 – About 75% of the data falls below this value Interquartile Range (IQR) – the difference between Q3 and Q1.

Finding the Quartiles Section 2.5 Arrange the data in order from lowest to highest. Find the median of the data. (Q2) Find the median of the values to the left of the median. (Q1) Find the median of the values to the right of the median. (Q3)

Finding a Quartile Section 2.5 Find Q1, Q2, and Q3 for the data set: 15, 13, 6, 5, 12, 50, 22, 18

Finding an Outlier (1.5 Method) Section 2.5 Finding an Outlier (1.5 Method) Arrange the data in order to find Q1 and Q3. Find the IQR (Q3 – Q1) Multiply the IQR by 1.5 Lower Boundary: subtract that value from Q1 Upper Boundary: add that value to Q3. Check the data set for any value that is outside the boundaries.

Finding the Outlier Section 2.5 Check the following data set for outliers. 5, 6, 12, 13, 15, 18, 22, 50

Section 2.5 Boxplot – a graph of a data set obtained by drawing : a horizontal line from the minimum data value to Q1 a horizontal line from Q3 to the maximum data value a box whose vertical sides pass through Q1 and Q3 a vertical line inside the box passing through the median (Q2).

Section 2.5 Five Number Summary– the five specific values used to construct a boxplot. Minimum, the lowest value in a data set Q1 The median Q3 Maximum, the highest value in a data set

Determining the Five Number Summary Section 2.5 Determining the Five Number Summary A stockbroker recorded the number of clients she saw each day over an 11-day period. 33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31 Enter the data into L1 Calculate the 1-Var Statistics Scroll down to find your Five Number Summary

Creating a Boxplot Section 2.5 Draw an appropriate scale on a number line that contains values that span your five number summary Plot your five number summary above the number line. Draw a horizontal line from your minimum to Q1. Draw a horizontal line from Q3 to your maximum. Draw a box from Q1 to Q3. Draw a vertical line through your median.

How To Read a Boxplot Section 2.5 The median The lines (or “whiskers”) If the median is near the center of the box, the distribution is symmetric. If the median is to the left of the center of the box, the distribution is positively skewed. If the median is to the right of the center of the box, the distribution is negatively skewed. The lines (or “whiskers”) If the lines are about the same length, the distribution is symmetric. If the right line is larger, the distribution is positively skewed. If the left line is larger, the distribution is negatively skewed.

Homework Section 2.5 Pg. 109 (11 – 19 ODD) Read and take notes on Section 2.5 (pgs. 106-107)