Algorithm for Average of N numbers

1
Algorithm for Average of N numbers

• GIVENS
• X (An array of values)
• N (Length of array X)
• RESULTS
• Average (The average of the values in
  the array X)
• INTERMEDIATES
• Sum (Sum of array values)
• Index (Current position in array)
• HEADER
• Average ? FindAverage(X, N)

Sum ? 0Index ? 0
Index lt N ?
true
Sum ? Sum XIndex Index ? Index 1
false
Average ? Sum / N
2
Standard Deviation Algorithm (1)

• GIVENSX (an array containing a collection of
  real numbers)N (the length of the array)
• RESULTSStDev (the standard deviation of the
  values in the array)
• INTERMEDIATESSum (accumulates the sum of the
  array)SumIndex (used as array index to find sum
  of array)Average (average of array
  elements)DiffSqSum (accumulates the sum of the
  squares of the differences)DiffSqIndex (used
  as array index to find sum of squares of
  differences)
• HEADERStDev ? StandardDeviation(X, N)

3
Standard Deviation Algorithm (2)
Sum ? 0SumIndex ? 0
true
SumIndex lt N ?
false
Sum ? Sum XSumIndex SumIndex ? SumIndex 1
Average ? Sum / N DiffSqSum ? 0 DiffSqIndex ? 0
true
DiffSqIndex lt N ?
false
DiffSqSum ? DiffSqSum (XDiffSqIndex
Average) ? (XDiffSqIndex Average)
DiffSqIndex ? DiffSqIndex 1
StDev ? Sqrt( DiffSqSum / (N 1) )
4
Algorithm for Distance of Thrown Ball (1)

• GIVENS
• V (Initial velocity of the ball, in metres /
  second)
• RESULTS
• Range (An array of for how far the ball will
  travel for various angles. The values will be
  for 0 degrees up to 90 degrees, in increments
  of 10 degrees. Result is in metres)
• INTERMEDIATES
• G (Constant Acceleration due to gravity
  9.8 m/s2)
• DegToRad (Constant Degrees to radians
  conversion ? / 180)
• Theta (Current horizontal angle, in degrees)
• ThetaRad (Current horizontal angle, in radians)
• HEADER
• Range ? FindDistance(V)

5
Algorithm for Distance of Thrown Ball (2)
Theta ? 0G ? 9.8DegToRad ? ? / 180Range ?
MakeNewArray(10)
Theta 90 ?
true
false
ThetaRad ? Theta DegToRad RangeTheta/10 ? 2
V V sin(ThetaRad) cos(ThetaRad) / GTheta
? Theta 10