# Computing Arithmetic, Geometric and Harmonic Means

### Problem Statement

The arithmetic mean (i.e., average), geometric mean and harmonic mean of a set of n numbers x1, x2, ..., xn are defined as follows:

Since computing geometric mean requires taking square root, it is further required that all input data values must be positive. As a result, this program must be able to ignore those non-positive items. However, this may cause all input items ignored. Therefore, before computing the means, this program should have one more check to see if there are valid items.

### Solution

```! ----------------------------------------------------------
! This program reads a series of input data values and
! computes their arithmetic, geometric and harmonic means.
! Since geometric mean requires taking n-th root, all input
! data item must be all positive (a special requirement of
! this program , although it is not absolutely necessary).
! If an input item is not positive, it should be ignored.
! Since some data items may be ignored, this program also
! checks to see if no data items remain!
! ----------------------------------------------------------

PROGRAM   ComputingMeans
IMPLICIT  NONE

REAL    :: X
REAL    :: Sum, Product, InverseSum
REAL    :: Arithmetic, Geometric, Harmonic
INTEGER :: Count, TotalNumber, TotalValid

Sum        = 0.0                     ! for the sum
Product    = 1.0                     ! for the product
InverseSum = 0.0                     ! for the sum of 1/x
TotalValid = 0                       ! # of valid items

DO Count = 1, TotalNumber            ! for each item ...
WRITE(*,*) 'Input item ', Count, ' --> ', X
IF (X <= 0.0) THEN                ! if it is non-positive
WRITE(*,*) 'Input <= 0.  Ignored'   ! ignore it
ELSE                              ! otherwise,
TotalValid = TotalValid + 1    ! count it in
Sum        = Sum + X           ! compute the sum,
Product    = Product * X       ! the product
InverseSum = InverseSum + 1.0/X     ! and the sum of 1/x
END IF
END DO

IF (TotalValid > 0) THEN             ! are there valid items?
Arithmetic = Sum / TotalValid     ! yes, compute means
Geometric  = Product**(1.0/TotalValid)
Harmonic   = TotalValid / InverseSum

WRITE(*,*)  'No. of valid items --> ', TotalValid
WRITE(*,*)  'Arithmetic mean    --> ', Arithmetic
WRITE(*,*)  'Geometric mean     --> ', Geometric
WRITE(*,*)  'Harmonic mean      --> ', Harmonic
ELSE                                 ! no, display a message
WRITE(*,*)  'ERROR: none of the input is positive'
END IF

END PROGRAM  ComputingMeans
```

### Program Input and Output

This program uses the same format of input as discussed in previous example. More precisely, the first line gives the number of data items, followed by that number of input line on each which is a data value. Except for the first input value, which gives the number of input, all other values are real numbers.
• If the input data is
```5
1.0
2.0
3.0
4.0
5.0
```
it will generate the following output. In this input, all data values are positive and none of them is ignored.
```Input item 1 --> 1.
Input item 2 --> 2.
Input item 3 --> 3.
Input item 4 --> 4.
Input item 5 --> 5.

No. of valid items --> 5
Arithmetic mean    --> 3.
Geometric mean     --> 2.6051712
Harmonic mean      --> 2.18978071
```
• In the following input, the fourth value is negative.
```6
1.0
2.0
3.0
-4.0
5.0
6.0
```
The output is shown below:
```Input item 1 --> 1.
Input item 2 --> 2.
Input item 3 --> 3.
Input item 4 --> -4.
Input <= 0.  Ignored
Input item 5 --> 5.
Input item 6 --> 6.

# of items read --> 6
# of valid items -> 5
Arithmetic mean --> 3.4000001
Geometric mean  --> 2.82523465
Harmonic mean   --> 2.27272725
```
• Now, let us try the following input in which all values are non-positive:
```4
-1.0
-2.0
0.0
-3.0
```
We shall get the following output. The program correctly detects there is no valid data values and displays a message.
```Input item 1 --> -1.
Input <= 0.  Ignored
Input item 2 --> -2.
Input <= 0.  Ignored
Input item 3 --> 0.E+0
Input <= 0.  Ignored
Input item 4 --> -3.
Input <= 0.  Ignored

ERROR: none of the input is positive
```

### Discussion

This example is quite simple and does not require further explanation.