1 / 14

Chapter 10

Chapter 10. Introduction to Statistics. 10.1 Frequency Distributions; Measures Of Central Tendency. Grouped frequency distribution Histogram, Frequency polygon Stem and leaf Summation notation (sigma notation) x 1 + x 2 + x 3 + ….+ x n = The mean (arithmetic everage)

abrahambeverly
Télécharger la présentation

Chapter 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 Introduction to Statistics

  2. 10.1 Frequency Distributions; Measures Of Central Tendency • Grouped frequency distribution • Histogram, Frequency polygon • Stem and leaf • Summation notation (sigma notation) x1 + x2 + x3+ ….+ xn = • The mean (arithmetic everage) The mean of the n numbers x1, x2, x3, … xn is

  3. MEAN OF A GROUPED DISTRIBUTION • The mean of a distribution where x represents the midpoints, f the frequencies, and n= • Median: The middle entry in a set of data arranged in either increasing or decreasing order. If there is an even number of entries, the median is defined to be the mean of the two center entries. • Mode: the most frequent entry. If each entry has the same frequency, there is no mode.

  4. 10.2 MEASURES OF VARIATION • Range of a list of numbers: max – min • Deviations from the mean of a sample of n numbers x1, x2 , x3, … xn, with mean is: x1 – x2 – … xn –

  5. 10.2 MEASURES OF VARIATION SAMPLE VARIANCE • The variance of a sample of n numbers x1, x2 , x3, … xn, with mean , is s2 = Population variance: s2 =

  6. 10.2 MEASURES OF VARIATION SAMPLE STANDARD DEVIATION • The standard deviation of n numbers x1, x2 , x3, …, xn, with mean , is

  7. 10.2 MEASURES OF VARIATION STANDARD DEVIATION FOR A GROUP DISTRIBUTION • The standard deviation for a distribution with mean , where x is an interval midpoint with frequency f, and n =

  8. 10.3 NORMAL DISTRIBUTION • Continuous distributionOutcome can take any real number • Skewed distributionThe peak is not at the center • Normal distributionbell-shaped curve (4 basic properties) • Normal curvesThe graph of normal distribution

  9. 4 Basic Properties Of Normal Distribution • The peak occurs directly above the mean • The curve is symetric about the vertical line through the mean. • The curve never touches the x-axis • The area under the curve is 1 The mean: m Standard deviation: s Standard normal curve: m=0, s = 1

  10. AREA UNDER NORMAL CURVE There area of the shaded region under the normal curve from a to b is the probability that an observed data value will be between a and b.

  11. Z-score • z-score • If a normal distribution has mean  and standard deviation , then the z-score for the number is z =

  12. AREA UNDER NORMAL CURVE The area under normal curve between x=a and x=b is the same as the area under the standard normal curve between the z-score for a and the z-score for b.

  13. 10.4 Normal Approximation to the Binomial Distribution • The expected number of successes in n binomial trials is np, where p is the probability of success in a single trial. • Variance and standard deviation 2 = np(1 – p) and  =

  14. Suppose an experiment is a series of n independent trials, where the probability of a success in a single trial is always p. Let x be the number of successes in the n trials. Then the probability that exactly x success will occur in n trials is given by:

More Related