GTECH 201 Lecture 12 - PowerPoint PPT Presentation

About This Presentation
Title:

GTECH 201 Lecture 12

Description:

Intro to Descriptive Statistics GTECH 201 Lecture 12 Topics for Today Measures of Central Tendency Mean, Median, Mode Sample and Population Mean Weighted Means ... – PowerPoint PPT presentation

Number of Views:48
Avg rating:3.0/5.0
Slides: 28
Provided by: lax3
Category:

less

Transcript and Presenter's Notes

Title: GTECH 201 Lecture 12


1
GTECH 201Lecture 12
Intro to Descriptive Statistics
2
Topics for Today
  • Measures of Central Tendency
  • Mean, Median, Mode
  • Sample and Population Mean
  • Weighted Means
  • Selecting Appropriate Measures of Central
    Tendency
  • Measures of Dispersion
  • Variance
  • Standard Deviation

3
Descriptive vs. Inferential
  • Descriptive Statistics
  • Methods for organizing and summarizing
    information
  • Inferential Statistics
  • Methods for drawing and measuring the reliability
    of conclusions about a population based on
    information obtained from a sample of the
    population

4
Looking at This Data Set
5
Overview
  • Mean
  • Median
  • Mode
  • Sample and Population Mean
  • Weighted Means
  • Selecting Appropriate Measures of Central
    Tendency
  • Applying these measures

6
Mean
  • The mean of a set of n observations is the
    arithmetic average
  • Mean of n observations x1, x2,x3,.xn is

In Excel, AVERAGE(insert range)
7
Median
  • The data value that is exactly in the middle of
    an ordered list if the number of pieces of data
    is odd
  • The mean of the two middle pieces of data in an
    ordered list if the number of pieces of data is
    even
  • The median is a typical value it is the midpoint
    of observations when they are arranged in an
    ascending or descending order

8
Mode
  • The most frequent data value i.e., any value
    having the highest frequency among the
    observations
  • In Excel,you use the functions
  • MEDIAN (insert range)
  • MODE (insert range)
  • Unimodal, Bimodal, Multimodal data sets
  • Outliers

9
Sample and Population Means
  • Mean of a data set
  • Population mean if data set includes entire
    population
  • Sample mean if data set is only a sample of the
    population

10
Weighted Means
  • To calculate the mean when your information is
    available only in the form of summary data
  • C Interval Freq
  • 25 29.9 4
  • 30 34.9 5
  • 35 39.9 12

11
Skewed Distributions
12
Skewed Distributions
  • When there is one mode and the distribution is
    symmetric
  • mean, median, mode are the same
  • Positive skew
  • mean moves towards the positive tail
  • median also pulls towards the positive tail
  • Negative skew
  • mean moves towards the negative tail
  • median also moves towards the negative tail

13
Selecting Appropriate Measures
  • Mean
  • affected by extreme values
  • includes all observations, therefore
    comprehensive (useful for interval/ratio data)
  • Median
  • not affected by the number of observations
  • reveals typical situations (used for ordinal
    data)
  • Mode
  • useful for nominal variables

14
Other Useful Calculations
  • In addition to the sum of data, Sxwe need to be
    able to calculate

15
Variability or Spread
  • Mean and the median - limits
  • Range coarse measure of variability
  • Percentiles
  • kth percentile is the point at which k percent of
    the numbers fall below it and the rest are fall
    above it
  • 25th percentile (lower quartile)
  • 50th percentile (median)
  • 75th percentile (upper quartile)
  • Interquartile range (difference between the 25th
    percentile value and the 75th percentile value)

16
Describing the Spread
  • A five number summary
  • Median
  • Quartiles
  • Extremes
  • Variance and Standard Deviation
  • Measures spread about the mean
  • Standard deviation cannot be discussed without
    the mean

17
Calculating Percentiles
  • In the list of twelve observations
  • 4 7 11 11 11 11 14 16 16 24 29
  • Compute median, 25th and 75th percentiles

The lower quartile is the median of the 6
observations that fall below the median
The upper quartile is the median of the 6
observations that fall above the median
18
Five Number Summary
  • Median 11
  • Lower Quartile 9
  • Upper Quartile 16
  • Extremes are 2 and 29
  • Can compute the range 27
  • In a symmetric distribution, the lower and upper
    quartiles are equally distant from the median

19
Variance
  • Is the mean of the squares of the deviations of
    the observations from their mean
  • Population variance
  • Sample variance

20
Example
The heights, in inches for five starting players
in a mens college basket ball team
are 67 72 76 76 84 Compute the mean and
standard deviation.
75
21
Standard Deviation
  • Standard deviation is positive square root of the
    variance
  • Variance in our basketball example

39
22
Formulas Standard Deviation
Standard deviation of a sample
Standard deviation of a population
23
Example (Continued)
24
Short Cut Simpler Formula
Standard Deviation of a sample
Sum of the squares of data values, i.e., you
square each data value and then sum those squared
values
Square of the sum of data values, i.e., you sum
all the data values and then square that sum
25
Example (using the short cut)
26
Interpreting Std. Deviation
  • s and s 2 will be small when all the data are
    close together
  • The deviations from the mean
  • Will be both positive and negative
  • Sum will always be 0
  • s is always 0 or a positive number
  • s 0 means no spread as s value increases, the
    spread of the data increases
  • The units of s are the same as the original
    observations
  • s is heavily influenced by outliers

27
Coefficient of Variation
CV is the standard deviation described as a
percent of the mean
CV
CV is useful when comparing different sets of
data where sample size and standard deviation are
different
Write a Comment
User Comments (0)
About PowerShow.com