Stat 217 – Day 9 Topic 9: Measures of spread

Announcements HW 3 returned  Working on Lab 2 Topic 9 today and tomorrow Review on Wednesday  HWs, Labs discussion  Q and A discussion forum in Blackboard Exam (in lab) on Thursday  Review handout, problems posted Lab 4 to be started after exam

Last Time – Measures of Center Mean vs. Median  How to calculate  How to interpret “Balance point” vs. “typical” value  Resistance The University of North Carolina took a survey of the students who had graduated as geology majors. In 1986, the average annual salary of geology majors who graduated from UNC was more than $500,000.  The next year it was less than $100,000.

Activity 8-3 (p. 144) Symmetric: mean  median Skewed to the right: mean > median Skewed to the left: mean < median

Topic 8 Wrap up (p. 150) Mean and median are often similar but can differ  Median is resistant but the mean is not  Mean is pulled in the direction of the longer tail in a skewed distributions “The median is not the message”  Don’t forget about other aspects of the distribution  Don’t forget to graph the data!

Activity 8-6 Model Answer (a) half the houses more than the mean? The mean is going to be drawn towards the outliers, so we could not conclude that “half” the houses cost that. 100K 100K 100K 700K has mean 250K so ¼ cost more than the mean

Activity 8-6 Model Answer (b) total = median*5? This is wrong too because the median is resistant to outliers ,000 Median 600 but Total 3000

Activity 8-6 Model Answer (c) mean > 90% of data implies mistake? This could be wrong if high ranking employees earn far, far more than lower employees because outliers pull the mean 30, 40, 50, 60, 40, 45, 70, 30, 35, % < mean

Activity 8-6 Model Answer (d) mode implies more than 50%? Mode = most frequently occurring value Mode ≠ majority 10 people:: 4 chocolate, 3 strawberry, 3 vanilla Can’t consider mean or median here

HW questions?

Activity 9-3 (p. 166) Which class has more variability: class F or class G? Which class has more variability: class H, I, or J? Which has the least, H, I, or J?

Activity 9-1 Alternative a) Observational units/Response variable  Months/average temperature (b) Mean appropriate since symmetric with no outliers (c) The centers of the two distributions may be similar, but the Raleigh temperatures are definitely less consistent/more spread out

Measures of Spread (d) Range  San Francisco: 65 – 49 = 16 degrees  Raleigh: = 39 degrees (e) One extreme observation can greatly inflate the range

Measures of Spread Interquartile Range (IQR)  San Francisco Q u - Q L = 62.5 – 52.5 = 10 degrees 52.5 = “lower quartile”62.5 = “upper quartile”

Measures of Spread Interquartile Range (IQR)  San Francisco Q u - Q L = 62.5 – 52.5 = 10 degrees  Raleigh: Q u - Q L = 72.5 – 46.5 = 26 degrees (g) Not influenced by outliers

Measures of Spread Standard Deviation  San Francisco Feb Deviation: =-5.25 Feb Squared deviation: Sum of squared deviations = Actually divide by n-1 = Then square root =

Measures of Spread Standard Deviation  San Francisco = 5.75 degrees  Raleigh = degrees

Measures of Spread What about outliers? Caution: Range and Standard Deviation are not resistant

To turn in with partner  Activity 9-3(a)-(h) (p ) For Tuesday  Activity 9-3 (i), (j) - valuesFJ.xls  Activity 9-4  (HW 3 due Tuesday on Topics 7-9, keep copy?)

Lab 2 comments Careful in wording in describing bar graphs (k) focus on type of study – randomized experiment? (l) focus on how sample selected – random sample? (p) observational units and variable of the dotplot