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How to calculate the mean and standard deviation

Σ+ collects a list of numbers, then gx̄0 and gs. summarize it.

Problem

A fund returned 8.2%, −3.5%, 12.1%, 6.7%, 15.3% and −1.4% over six years. What were its average return and the standard deviation of returns?

Keystrokes

  1. fΣSST
    0.00

    Clears the statistics registers.

  2. 8.2Σ+
    1.00

    The first value. The display counts the entries.

  3. 3.5CHSΣ+
    2.00

    A negative value.

  4. 12.1Σ+
    3.00
  5. 6.7Σ+
    4.00
  6. 15.3Σ+
    5.00
  7. 1.4CHSΣ+
    6.00

    Six values entered.

  8. gx̄0
    6.23

    The mean.

  9. gs.
    7.40

    The sample standard deviation.

Answer

The average return is 6.23% and the standard deviation is 7.40%.

Why it works

Σ+ keeps running sums in registers R1 to R6: the count, the sum, the sum of squares, and so on. gx̄0 and gs. work from those sums, so the list can be as long as you like.

gs. is the sample standard deviation, which divides by n − 1. For a whole population, add the mean to the data with Σ+ once, then press gs. again.

Fixing a mistake

Key the wrong value again and press gΣ−Σ+ to take it back out.

Questions

Is the average return the compound return?

No. The arithmetic mean overstates compound growth when returns vary. For that, use the CAGR guide on the start and end values.

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