The population of eight analysts at a software firm were asked to estimate the reuse rate when developing a new software system. The following data are given as a percentage of the total code written for a software system that is part of the reuse database.

50, 62.5, 37.5, 75.0, 45.0, 47.5, 15.0, 25.0

What is the variance of the total code that is part of the reuse database?

Question

The population of eight analysts at a software firm were asked to estimate the reuse rate when developing a new software system. The following data are given as a percentage of the total code written for a software system that is part of the reuse database.

50, 62.5, 37.5, 75.0, 45.0, 47.5, 15.0, 25.0

What is the variance of the total code that is part of the reuse database?

BlackTom AI · Accepted Answer

We are given eight data points representing percentages of total code reused: 50, 62.5, 37.5, 75.0, 45.0, 47.5, 15.0, 25.0. The task is to find the variance of the total code that is part of the reuse database.

First, determine whether to treat these eight values as the entire population or as a sample. The prompt describes them as a population of eight analysts, so we will compute the population variance, which uses the denominator N (not N−1).

Step 1: Compute the mean (average) of the data.
- Sum = 50 + 62.5 + 37.5 + 75 + 45 + 47.5 + 15 + 25 = 357.5
- Number of observations N = 8
- Mean = 357.5 / 8 = 44.6875

Step 2: Compute each deviation from the mean and square it.
- 50: deviation 5.3125; square 28.22265625
- 62.5: deviation 17.8125; square 317.28515625
- 37.5: deviation −7.1875; square 51.66015625
- 75: deviation 30.3125; square 918.84765625
- 45: deviation 0.3125; square 0.09765625
- 47.5: deviation 2.8125; square 7.91015625
- 15: deviation −29.6875; square 881.34765625
- 25: deviation −19.6875; square 387.59765625

Step 3: Sum the squared deviations.
Sum of squared deviations = 28.22265625 + 317.28515625 + 51.66015625 + 918.84765625 + 0.09765625 + 7.91015625 + 881.34765625 + 387.59765625 = 2592.96875

Step 4: Divide by N to obtain the population variance.
Variance = 2592.96875 / 8 = 324.12109375

Conclusion (the computed value): The variance of the total code that is part of the reuse database is 324.12109375.

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