Statistics Chapter 3: Numerical Summaries of Center and Variation

is the value that occurs with the greatest frequency, can be used for both quantitative and qualitative data, is useful for predicting future results

the balancing point, the half-way point

the balancing point of a distribution of data, mean splits the value, when the distribution is symmetric it becomes the typical value, when it is not symmetric, the balancing point won't be center for this

X bar=Ex/n-X bar is the mean-E is the greek capital sigma which stands for summation -n is the number of observations

How much spread if from the center/typical point? The average distance from the average, has the same unit as the mean, effected by outliers

The sample standard deviation will have n-1 but the standard deviation will not-Find the meanx-mean (the deviation)to make all the numbers positive you (x-mean)2then add all the numbers found by the last stepdivide by n (the number of observations)square root it

standard deviation squaredthe unites used to measure spread are different from the units used to measure center

to compare two different graphs you can use the standardized deviation if it is unimodal and symmetric-about 68% fall within one standard deviation of the mean-about 95% fall within two standard deviations of the mean-nearly all fall within three standard deviations of the mean

Measures a value relative to the sample rather than with respect to some absolute measure, like the Z-score

Enables us to compare observations in one group with those in another, even if the two groups are measured in different units

Splits into frequency with 50% above and below, represents the typical value, resistant to outliers, Q2 2nd StatOps1: Sort A (means ascending) OR 2: Sort D (means descending)

Q3-Q1

The length of the box in a boxplot is proportional to the IQR.

The left edge of the box is at the first quartile and the right edge is at the third quartile the whiskers extend to the most extreme values that are not potential outliers. Potential outliers are then represented by others markers, such as dots.• Not always the smallest/largest value

If the median is near the center of the box and each horizontal line is of approximately equal length, the distribution is roughly symmetric. If the median is to the left of the center of the box and the right line is substantially longer than the left line, the distribution is skewed right.

If the median is to the right of the center of the box and the left line is substantially longer than the right line, the distribution is skewed left. If none of the previous conditions exists, the distribution does not have a defined name.

(IQRx1.5) +/- Q3 or Q1

o The minimum, Q1, the median, Q3, and the maximum