Box Plots

Statistical Measures Measures of Central Tendency: numbers that represent the middle of the data (mean, median, mode) Mean ( x ):Arithmetic average Median: Middle of the data listed in ascending order (use if there is an outlier) Mode:Most common number (if modes – can be more than one) Statistics  practice of analyzing a set of data Skewed Right (positively): Skewed Left (negatively): Less data to the right. Less data to the left Standard Deviation (σ): Variance: How much data is spread out Measure of variation (high=spread out)

5 Number Summary: Minimum Value (0 Percentile) Q1:Quartile 1 (25 th Percentile) Med (Q2):Median (50 th Percentile) Min: Q3:Quartile 3 (75 th Percentile) Max:Maximum or Q4 (100 th Percentile) Middle 50% Q1Q2 Med Q3 Max Q4 Min IQR: Q3 – Q1 (where the middle 50% are) 25%25% 25%25% 25%25% 25%25%

Mean Standard Deviation Minimum 1 st Quartile Median 3 rd Quartile Maximum Calculator Information You still have to find the mode by looking for the most common number(s), calculate the IQR by finding the diffference of Q3 and Q1 and finding the range by finding the difference of maximum and minimum Calculator Commands Enter data into STAT  EDIT STAT→CALC → 1-Var STATS…

Make the 130 a 120 and the 156 a 166. Recalculate What changed? Why? Listed below are the weights of 10 people (in pounds) 130, 150, 160, 145, 142, 143, 170, 132, 145, 156 Find the mean: mode: standard deviation median: minimum: 1 st quartile: 3 rd quartile: maximum IQR: Range: Make a box plot: Skewed: Q3-Q1: =14 Max-min: =40 Right (positive) Standard deviation, Range The data is more spread out

Class Data set of “The day of the month you were born on” Find the mean: mode: standard deviation median: minimum: 1 st quartile: 3 rd quartile: maximum IQR: Range: Make a box plot: Skewed:

The following is the amount of black M&M’s in a bag: 12, 13,14, 15, 15, 16, 17, 20, 21,22,23,24,25 Find the mean and standard deviation The following is the amount of black M&M’s in a bag: 9, 10,11, 14, 15, 16, 17, 20, 21,23,26,27,28 Find the mean and standard deviation Mean: Standard Deviation: 4.28 Mean: Standard Deviation: 4.28 Explain why the means are the same but the standard deviation is larger for the 2 nd example. The data is more spread out although it’s the same average.

Test Scores (n=60) 1.Between what scores do the middle 50% lie? 2.Between what scores does the lowest 25% lie? 3.Which range of scores has more density? (more numbers in a smaller number) 4. Estimate how many people got between 85-89? 5. Estimate how many people got below an 85? 6. What is the IQR? 7. What percentile did a person with a 70 get? %25% 25%25% 25%25% 25%25% *0.25 = = 19 25

Box plot of 80 Bowlers 1)What is the maximum score? 2)What is the IQR? 3)What percentage of bowlers got above a 85? 4)How many bowlers got below a 100? 5)What percentile did a 120 get? 6)Between what scores did the top 25% get? 7)Where are there less density of bowlers? 25%25% 25%25% 25%25% 25%25% 80*.25= = = = 40 75% (75% are below)

1)Which date has the most variability (spread)? 2)Make a statement about airline delays 3) Which would you expect to have larger variability (IQR) A) Heights of freshmen B) Ages of freshmen C) Weights of freshmen D) Heights of 5 year-olds?

[Which of the following will have the most variability? A.[Heights of people in this room] B.[Ages of people in this room] C.[The number of countries that people have been to in this room?] Variability: How close the numbers are together More spread out= High Variability = Large Standard Deviation =High IQR

Which would have a lower standard deviation? (Be prepared to explain): A.[The heights of students in this class] B.[The heights of students in this school]

Normal Distribution Bell Curve

Number of Shoes Owned per Person Frequency >268 Determine if the following examples are Normally Distributed, Positively Skewed, or Negatively Skewed.

Place the following under negatively skewed, normally distributed, or positively skewed, or random? A)The amount of chips in a bag B)The sum of the digits of random 4-digit numbers? C)The number of D1’s that students in this class have gotten? D)The weekly allowance of students E)Age of people on a cruise this week F) The shoe sizes of females in this class

Debate: Side 1) You are trying to convince your teacher to always curve test grades to a standard deviation Side 2) You are trying to convince your teacher to never curve test grades to a standard deviation

The next few slides are done as a wrap up or warm-up the next few days There are three at the end for easy questions

Mode: Most often number. Mean: Average. Median: The middle number when arranged from smallest to largest. Best to show when there are outliers!!! 1) Find the mode, mean, and median: 5,7,9,9,30 2) Which is the largest? 3) Now include a 90 in the data. Which of the three changed the most? 4) When they list salaries, why do they state the median price and not the mean price? Mean Mean: It went from 12 to 25 Median is less affected by outliers

City statsBest places avg. Median family income (per year) $55,755$96,825 Job growth % ( )* 6.99%25.01% Median home price$120,000$269,768 Test scores reading (% above/below state average) -11.7%28.2% Test scores math (% above/below average) -2.3%29.2% Personal crime incidents (per 1,000)72 Property crime incidents (per 1,000)5720 Restaurants (within 15 miles) 1,5563,134 High temp in July ° F88.1°86.8° Low temp in Jan ° F25.4°18.4° Median age Stats for Winston-Salem stats (Rated #10 as best place to live by Money Magazine)

Deeper Understanding Suppose there are 20 tests and the scores are all an 80%. What would change if 2 more tests were added that were both a 90%, mean or median? What if there were 20 tests, 4 were 70%, 12 were 80%, and 4 were 90%. Three more tests were added to group scoring 70%, 90%, and 100%. How would the mean or median change?

Trick or Treat Ten neighborhood kids went out to get candy. Here is a list of the number of treats they received: 45, 34, 56, 32, 10, 32, 62, 11, 55, 34 a.Find the mean, median, and IQR of the treats. b.The kid who got 62 treats, went back out and got 262 treats. Find the new mean, median and IQR. c.Which does a better job of describing the typical number of treats for the new data? Why? d.Draw a box plot.

Suppose you wanted to open restaurants. 1.Where would you put a few of them? 2.Where would you want a lot of them? Which way is the data skewed?

Ex. Find the mean, median, and mode of 85, 76, 88, 91, 85, 58, 88, 91, 97, 91, 88, 97, 97 Mean ( ) = median =, mode = Draw a box plot of the data.

FIVE-NUMBER SUMMARY: Find the 5 number summary and draw a box plot. Maria: 8, 9, 6, 7, 9, 8, 8, 6, 9, 9, 8, 7, 8, 7, 9, 9, 7, 7, 8, 9 Min.: Q1: Q2 (median): Q3: Max.: Interquartile Range (IQR): Q3 – Q1= – 7 =

FIVE-NUMBER SUMMARY: Gia: 8, 9, 9, 9, 6, 9, 8, 6, 8, 6, 8, 8, 8, 6, 6, 6, 3, 8, 8, 9 Min.: Q1: Q2 (median): Q3: Max.: Interquartile Range (IQR): Q3 – Q1= – 6 = 2.5 Find the 5 number summary and draw a box plot