Statistical Measures

This program computes a comprehensive set of descriptive statistics for a user-supplied dataset of up to 100 values. It calculates arithmetic mean, median, mode (including multiple modes), standard deviation, variance, minimum, maximum, and range. Data entry ends when the user inputs the sentinel value 9999, and an interactive correction loop lets the user amend any numbered item before processing. Sorting is performed in-place using a straightforward O(n²) selection-style sort, and the mode is detected by scanning the sorted array for runs of equal values using a parallel count array.

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Program Analysis

Program Structure

The program is organized as a main routine with six subroutines, each handling a distinct processing stage. The main routine (lines 20–310) drives the flow sequentially, calling each subroutine in order.

1. Lines 20–80: Initialization — sets constants, dimensions arrays, prints header.
2. Lines 90–140: Data entry loop, terminated by sentinel value L=9999.
3. Lines 150–230: Main dispatch — optional data print/correct, then calls all computation subroutines.
4. Lines 330–520: Subroutine — print and optionally correct data items.
5. Lines 540–600: Subroutine — compute arithmetic mean (S1).
6. Lines 620–720: Subroutine — sort data array in ascending order.
7. Lines 740–810: Subroutine — compute median (S2).
8. Lines 830–1030: Subroutine — compute mode (S3), supporting multiple modes.
9. Lines 1050–1120: Subroutine — compute standard deviation (S4) and variance (S5).
10. Lines 1140–1360: Subroutine — print all results.

Data Entry and Correction

The entry loop (lines 90–130) pre-fills each slot with L (9999) at line 100, then immediately overwrites it with INPUT D(I) at line 110. The sentinel check at line 120 exits the loop early. The actual count of entered values is stored in I1 = I - 1 at line 140.

The correction subroutine (lines 330–520) reprints the numbered list and prompts for an item number to change. Entering 0 exits the correction loop (line 480). This loop repeats until the user explicitly answers “N” to the correction prompt.

Sorting Algorithm

The sort subroutine (lines 640–710) uses a nested-loop comparison sort. For each pair (I, J) where J > I, it swaps elements if D(I) > D(J), using DO as a temporary variable. This is effectively a selection/bubble hybrid with O(n²) complexity, appropriate for the 100-item maximum.

Median Calculation

After sorting, the median subroutine (lines 760–800) checks whether I1 is even by comparing INT(I1/2) with I1/2. For an even count it averages the two middle elements; for an odd count it selects the central element. Note the off-by-one pattern: for odd I1, T6 = INT(I1/2) and the median is D(T6+1), which correctly indexes the middle element in 1-based arrays.

Mode Calculation and Multiple Modes

The mode subroutine (lines 850–1030) exploits the sorted order to count consecutive runs. A sentinel D(I1+1) = L is appended to force a final run flush. The count of each run is stored in parallel array C, and C9 tracks the maximum run length. A second pass then collects all data values whose run count equals C9, storing successive modes in S3 with counter K. The results loop at line 1250–1270 prints all K-1 modes.

Notable Bugs and Anomalies

• Uninitialized accumulators: S1, T8, CO, and C9 are never explicitly initialized to zero; the program relies on the interpreter’s default of zero for unset numeric variables. This works in practice but is fragile if the program were restarted without a full NEW.
• Variable name collision — C0 vs CO: Line 940 uses LET C0=1 (digit zero) while lines 960 and 920 use CO (letter O). In Sinclair BASIC, variable names are single characters, so C0 and CO are distinct variables. The counter is incremented as CO but reset as C0, meaning the reset never affects the variable being counted — this is a genuine bug that will cause incorrect mode counts across different run values.
• SUM printed as MEAN: Line 1200 labels S1 as “SUM” but by that point S1 has already been divided by I1 in the mean subroutine (line 590), so it actually prints the mean twice — once labelled “SUM” and again labelled “MEAN” at line 1220.
• DIM S(M4) at line 75: The array S is dimensioned to 10 but never used anywhere in the program; it appears to be a vestigial artifact.
• Variance label: The standard deviation computed at line 1110 is the population standard deviation (dividing by I1, not I1-1), which is mathematically consistent with the population variance at line 1100.

Key Variables Summary

Variable	Role
D()	Data array, max 100 elements
I1	Actual count of entered values
S1	Arithmetic mean
S2	Median
S3	Mode (last found)
S4	Standard deviation
S5	Variance
C9	Maximum run frequency (for mode)
K	Number of modes found
L	Sentinel value (9999)
X$	Decorative separator line