An IT company develops software for the banking sector. It tests its code using an industry standard software package. Aiming to expand its business and be more competitive in the sector, the company has decided to pilot an in-house software package to test its code. A company researcher wishes to compare the times taken for each package to complete tests. Both software packages were run on 20 occasions testing the same code. The researcher records the times taken on each occasion, and these are shown in Table 1. Table 1 Comparison of test times in minutes for the industry standard and in-house software testing packages Test number Industry standard software package In-house software package 1 357 325 23 337 335 344 310 4 402 354 567 376 318 398 337 304 328 8 368 335 9 656 337 10 382 355 11 310 318 12 354 339 13 387 347 14 391 351 15 366 335 16 376 348 17 316 325 18 349 332 19 392 354 20 386 344 (b) Spend a few minutes scanning these datasets by eye. (i) List any three features that you should be looking for when scanning datasets by eye. (ii) Comment on whether or not you think there might be a problem with any of the most extreme values in each column. (c) Copy and complete the following table using the datasets given above to work out the missing values. Number of minutes to complete the test Industry standard In-house Minimum (Min) Lower quartile (Q1) 346.5 326.5 Median 372 336 Upper quartile (Q3) 389 347.5 Maximum (Max) Mean 377.55 336.35 Standard deviation (SD) 69.88 12.69 Interquartile range (IQR) Range Size of dataset (n) 20 20 (d) (i) Identify the two measures of location from the table in part (c). Use both of these measures to determine which of the two datasets has the higher location. (ii) Identify the three measures of spread from the table in part (c). Which of the two datasets has the wider spread, as measured by each of these three measures? (e) (i) The researcher concludes that the in-house software package runs quicker than the industry standard software package. Is this a reasonable conclusion? Explain your answer briefly. (ii) Which stage of the statistical investigation is used in part (e)(i)? Briefly justify your answer. (f) The researcher notices that the industry standard software package entry for the ninth test was a typing error. The correct value should have been 356. The revised mean and median for the industry standard software package data with the correct value for the ninth test are given in the following table. Industry standard software package With typing error With correct value Mean Median 377.55 372 362.55 367 What is the effect on the mean and on the median of including the typing error instead of the correct value? Explain why this happens. (g) Would having the correct value affect the researcher's conclusion in part (e)(i)? Explain your answer briefly.