Midterm Reviewer

• Measures of Central Tendency


  • A single value that represents a data set
  • Purpose is to locate the center of a data set
  • Commonly referred to as an average
  • Common measures: mean, median, mode

  
• Mean


  • There is only one mean in the data set
  • Applied for interval and ratio data
  • All values in the data set are included
  • Useful in comparing two or more data sets
  • Affected by the extreme small or large values on a data set
  • Cannot be computed if the frequency is an open-ended class

  
• Arithmetic Mean


  • The only common measure
  • All values in the given data set must be considered to determine its value
  • Symbols: x̄ (X bar) for sample, μ (mu) for population

  
• Arithmetic Mean Formula


  1. Sample mean: x̄ = ∑x/n

  2. Population mean: μ = ∑x/N

  
• Mean of Grouped Data Formula

  1. Sample mean: x̄ = ∑fx/n

  2. Population mean: μ = ∑fx/N

  3. f = frequency and x = midpoint

  
• Differences of Grouped and Ungrouped Data

  • Grouped data: presented in frequency data, classified into classes
  • Ungrouped data: whether arranged or unarranged, still an ungrouped data
• Weighted Mean


  • Useful when various classes of groups contribute differently to the total
  • Found by multiplying each value by its corresponding weight and dividing by the sum of the weights
• Weighted Mean Formula


  x̄w = ∑(wiXi)/∑wi = (w1X1 + w2X2 + ... + wnXn)/(w1 + w2 + ... + wn)
• Geometric Mean


  • To determine the average percents, indexes, and relatives
  • To establish the average percent increase in production, sales, or other business transaction or economic series from one period of time to another
• Geometric Mean Formula


  1. GM = ∛(x1*x2*x3*...*xn)

  2. GM = ∛(value at the END of the period/value at the START of the period) - 1
• Combined Mean


  The grand mean of all the values in all groups when two or more groups are combined
• Combined Mean Formula


  x̄CM = ∑(NiX̄i)/∑Ni = (N1X̄1 + N2X̄2 + ... + NnX̄n)/(N1 + N2 + ... + Nn)
• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• Median


  • The midpoint of the ordered data array
  • There is only one median
  • Data levels used are ordinal, interval, ratio
  • More valuable in an ordinal type of data

  
• The Wealth of Nations was written

  1776
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• STATISTICAL ANALYSIS AND SOFTWARE APPLICATION
• Properties of Median


  • Unaffected by extreme values
  • Useful when data is skewed
  • Divides the data into two equal parts

  
• GARCIA, NARLAINE O. – BACHELOR OF SCIENCE IN ACCOUNTANCY
• 2ND SEMESTER │A.Y. 2023 - 2024
• Course Outline


  • Dispersion
  • Measures of Dispersion
  • Measures of Location
  • Coefficient of Variation
  • Chebyshev's Theorem
  • Empirical Rule
  • Kurtosis
  • Coefficient of Skewness
  • Outliers
  • Boxplot (Box-and-Whisker plot)
  • Effects of Changing Units
• Dispersion


  Difference between the actual value and the average value
• Range


  Difference between the highest value and the lowest value in the data set
• A study comparing the typical household incomes for 3 districts in the City of Manila was initiated to see where differences in household incomes lie across districts
• Mean household income


  The average household income for a sample of families in a district
• The mean household incomes for a sample of 45 different families in three districts of Manila are shown in the following table
• Example


  • The daily rates of a sample of eight employees at GMS Inc. are ₱550, ₱420, ₱560, ₱500, ₱700, ₱670, ₱860, ₱480. Find the range.
• Districts


  • District 1
  • District 2
  • District 3
• Average Deviation


  The absolute difference between the element and a given point
• AD for Ungrouped Data

  Population AD: ∑/X - μ/ / N

  Sample AD: ∑/X - x̄/ / n

  X= individual value
• Example


  • The daily rates of a sample of eight employees at GMS Inc. are ₱550, ₱420, ₱560, ₱500, ₱700, ₱670, ₱860, ₱480. Find the average deviation.
• The combined mean household income for all 45 families in the Manila sample is 33,193.33
• AD for Grouped Data

  Population AD: ∑ f/X - μ/ / N

  Sample AD: ∑ f/X - x̄/ / n

  X= individual value; f = frequency
• The median is the midpoint of the ordered data array
• Median


  • Unique, there is only one median
  • Found by arranging the set of data from lowest to highest (and vice versa) and getting the value of the middle observation
  • Not affected by the extreme small or large values
  • Can be computed for an open-ended frequency distribution
  • Can be applied for ordinal, interval, and ratio data

  
• Example


  • The data below shows the frequency distribution of the amounts of electric consumption of a typical household in Batangas City for the month of January 2009. Find the average deviation.

  Amount of Electric Bill

  Number of Families

  700 – 849

  850 – 999

  1,000 – 1,149

  1,150 – 1,299

  1,300 – 1,499

  2

  9

  15

  9

  5
• Calculating median for ungrouped data

  1. If n is odd, the median is the middle ranked

  2. If n is even, then the median is the average of the two middle ranked values

  3. Formula: Median (Rank Value) = (n+1)/2th