1. 13.2: Measuring the Center and Variation of Data Kalene Mitchell Allie Wardrop Sam Warren Monica Williams Alexis Carroll Brittani Shearer

2. Common Core Standards  Summarize and describe distributions.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  CCSS.MATH.CONTENT.6.SP.B.5.C  Grade 6

3. The Mean…  Definition: The mean or average, of a collection of values is x ̅ = S/n, where S is the sum of the values and n is the number of values. The symbol x ̅ should read as “x bar.”  Commonly referred to as:  Average  Arithmetic mean

4. The Mean…  Example: Find the mean of the following values: 13, 18, 13, 14, 13, 16, 14, 21, 13

5. Page 735  All 12 players on the Uni Hi basketball team played in their 78- to-65 win over Lincoln. Jon Highpockets, Uni Hi’s best player, scored 23 points in the game. How many points did each of the other players average?

6. The Median…  Let a collection of n data values be written in order of increasing or decreasing size.  Largest # Smallest #  Half values above & half values below  Can be used in situations where we cannot get a proper measurement but can only rank data in order  ex: Arrange workers in order of their performance.  A worker in the middle would represent median performance.  50% of the workers do not work as hard  50% of the workers work harder

7. The Median…  If n is odd, the median, denoted by x, is the middle value in the list.  X= middle Value  If n is even, x is the average of the two middle values. The symbol x should be read as “x hat.”  X= n1 (first middle #) + n2 (second middle # / 2) ^ ^ ^

8. The Median…  Example: Find the median of the following values: 11, 13, 5, 19, 33, 12, 14, 15, 16, 11, 10, 32  If we take away one values, how would it change the problem? 11, 13, 5, 19, 33, 12, 14, 15, 16, 11, 10

9. The Mode…  Definition: A value that occurs most frequently in a collection of values.  If two values occur equally often and more frequently than all other values, there are two or more modes. (Bi….Tri…)  Commonly referred to as:  The number seen most often

10. The Mode..  Example: Find the mode of the following values: 44, 35, 36, 43, 41, 40, 35, 37, 34, 36, 37, 33, 36

11. Measures of Variability  Variability- how far spread out the scores or data points are  There are four frequently used measures of variability  Range: highest minus lowest score  Interquartile range- range of middle 50% scores  Standard deviation  Variance

12. Upper and Lower Quartiles  Definition: Consider a set of data arranged in order of increasing size. Let the number of data values, n, be written as n=2r when n is even, or n=2r+1 when n is odd, for some integer r.  The lower quartile, denoted by QL, is the median of the first r data values.  The upper quartile, denoted by Qu, is the median of the last r data values.

13. Page 737  For the given data set of this problem, determine the lower and upper quartile.  A = (12,7,14,15,9,11,10,11,0,8,17,5)

14. Interquartile Range IQR  Definition: Difference between the upper and lower quartile  IQR= Qu - QL  In other words: 75 th percentile – 25 th percentile

15. Outlier  Definition: data value that is LESS THAN QL –(1.5 x IQR) or GREATER THAN +(1.5 x IQR)  In other words, data points or scores that are atypical of the other values in the data set.  So less than 25 th percentile – (1.5 x 75 th percentile)  Or greater than 75 th percentile – (1.5 x 25 th percentile)

16. Box Plot or Box-and-Whisker Plot  Definition: consists of a central box extending from the lower to the upper quartile, with a line marking the median and with line segments, or whisker, extending outward from the box to the extremes.

17. Standard Deviation  Definition: Let X1, X2, X3…..Xn be the values in a set of data and let x denote their mean.  What it means- How far from the normal  Formula:

18. How to Find Standard Deviation  Step 1: Find the mean  Step 2: Find the difference each number is from the mean  Step 3:Take each difference and square it  Step 4: Add those numbers together  Step 5: Divide that sum by the total number of terms  Step 6:Take the square root of that number