Warm Up Find the median of the following data set. Car accidents on Main and First street during the past 7 years

Chapter 2.5 Notes Measures of Position

Fractiles Fractiles are numbers that partition or divide an ordered data set into equal parts. There are a lot of different fractiles. Quartiles Quartiles are fractiles that partition the data sets into 4 equal parts. The three quartiles are Q1, Q2 and Q3.

Q2 To find Q2 you just have to find the median of the data set Q2 = 5 To find Q1 take the first half of the data and find the median Q1 Q1=2

To find Q3 you must take the second half of the data and find the median of that Q3Q3= Q1 Q2 Q3

Box and Whisker Plot Min = 1 Q1 = 2Q2 = 5Q3 = 9 Max = 15 Min Max

Example 1 Find Q1, Q2 and Q3 and construct a box and whisker plot

Inter-quartile Range This calculates the range of the box in the box and whisker plot. IQR = Q3 – Q1

Warm Up Create a box and whisker plot for the following data set. Amount of money made per hour by 9 individuals $11.25$9.50$10.75$24.80 $12.30$16.75$42.25$62.85 $18.00

Types of fractiles Quartiles : Divide data into 4 equal pieces Deciles: Divide data into 10 equal pieces Percentiles : Divide data into 100 equal pieces

Standard Score/Z-Score -A z-score can be negative, positive or zero. -Z-score represents the number of standard deviations a given value x falls from the mean. z = value – mean_____ = x - µ Standard Deviation σ Page 92 for more info

Example 1 X = 15 µ = 12 σ = 2

Example 1 X = 15 µ = 12 σ = 2 Z = 15 – 12 = 3 = 1.5 2

Example 2 x = 8.2 µ = 25.3 σ = 7.5