EXAM TOMORROW Aim: Review for Exam. Properties of Standard deviation SD measures the spread about the mean and should be used only when the mean is chosen.

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Presentation transcript:

EXAM TOMORROW Aim: Review for Exam

Properties of Standard deviation SD measures the spread about the mean and should be used only when the mean is chosen as the measure of center. The larger the standard deviation, the more disperse, or spread out, the distribution is.

Summary of the Properties of the Theoretical Normal Distribution Normal Distribution: is a continuous, symmetric, bell shaped distribution of a variable. The mean, median and mode are equal and located at the center of the distribution. Curve never touches the x-axis but gets increasingly closer.

Population variance and Standard deviation Population Variance/Standard Deviation - measures the variability of data in a population VARIANCESTANDARD DEVIATION

Sample Variance and Standard Deviation Sample Variance/Standard Deviation - measures the variability of data in a sample - Usually based on a small and manageable sample size VARIANCESTANDARD DEVIATION

Different Distributions Bimodal Distribution J-Curve

Group Frequency Distribution Procedure: 1. Find class limits: 1. Find range of data 2. Find the width (range divided by number of classes)  always an odd number 2. Find class boundaries: (one decimal place more) 1. Add 0.5 to upper class limit 2. Subtract 0.5 to lower class limit 3. Fill in tally, frequency and cumulative frequency

Example Class Limit Class Boundaries TallyFrequencyCumulative Frequency // //// /// //// //// //// /// //// //// /// //// // / /150

Finding the Class Midpoint Class Midpoint:  obtained by adding the lower and upper boundaries and dividing by 2 OR  adding the lower and upper limits and dividing by 2. Lower limit + Upper limit 2 Lower boundary + Upper boundary 2

Finding Outliers 1. Find the first quartile and third quartiles 2. Find the IQR (third quartile – first quartile) 3. Multiply IQR by Find Boundaries 1. First Quartile – Step 3 2. Third Quartile – Step 3 5. Any data below Step 4-1 or above Step 4-2 are outliers

EXAM TOMORROW Aim: Review for Exam

Review Sheet Question #1 Class LimitClass Boundaries TallyFrequencyCumulative Frequency

Review Sheet Question #2 Find the range, variance and standard deviation of the following data. Assume that the data represents a sample of the population. 32, 36, 46, 20, 32, 18, 16, 34, 26, 27, 26

Review Sheet Question #3 Check the data for outliers: 14, 18, 27, 26, 19, 13, 5, 25

Review Sheet Question #4 A dietitian is interested in comparing the sodium content of real cheese with the sodium content of a cheese substitute. The data for two random samples are shown. Compare the distributions, using boxplots. Real Cheese 310, 420, 45, 40, 220, 240, 180, 90 Cheese Substitutes 270, 180, 250, 290, 130, 260,

Review Question #5 a. What is incorrect about the construction of the frequency distribution below? b. Find the midpoint of the first class below using the midpoint formula: ClassFrequency