How to describe a graph Otherwise called CUSS

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Presentation transcript:

How to describe a graph Otherwise called CUSS Do after Features of Distributions Activity

4. Spread discuss the variability of the data (how spread out it is) Range, IQR, standard deviation Pick the variability measurement that makes most sense. (ie Sometimes IQR means more than range)

Variability

Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability scores on standardized tests time bombs medicine

Measures of Variability range (max-min) interquartile range (Q3-Q1) deviations variance standard deviation Lower case Greek letter sigma

Suppose that we have these data values: 24 34 26 30 37 16 28 21 35 29 Find the mean. = 28 Find the deviations. What is the sum of the deviations from the mean?

24 34 26 30 37 16 28 21 35 29 Square the deviations: Find the average of the squared deviations:

The average of the deviations squared is called the variance. parameter statistic Population Sample

Calculation of variance of population

Calculation of variance of a sample df

A standard deviation is a measure of the average deviation from the mean.

Calculation of standard deviation for population

Calculation of standard deviation for a sample

Degrees of Freedom (df) n deviations contain (n - 1) independent pieces of information about variability

Which measure(s) of variability is/are resistant? IQR

Linear transformation rule When multiplying or adding a constant to a random variable, the mean changes by both. When multiplying or adding a constant to a random variable, the standard deviation changes only by multiplication. Formulas:

An appliance repair shop charges a $30 service call to go to a home for a repair. It also charges $25 per hour for labor. From past history, the average length of repairs is 1 hour 15 minutes (1.25 hours) with standard deviation of 20 minutes (1/3 hour). Including the charge for the service call, what is the mean and standard deviation for the charges for labor? Labor Charge = 30 + 25 (x), x= time of repair

Rules for Combining two variables To find the mean for the sum (or difference), add (or subtract) the two means To find the standard deviation of the sum (or differences), ALWAYS add the variances, then take the square root. Formulas: If variables are independent

Bicycles arrive at a bike shop in boxes Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the times for each setup phase are independent with the following means & standard deviations (in minutes). What are the mean and standard deviation for the total bicycle setup times? Phase Mean SD Unpacking 3.5 0.7 Assembly 21.8 2.4 Tuning 12.3 2.7