Test number Industry standard software package In-house software package

1 349 318

2 332 327

3 336 303

4 395 337

5 368 311

6 391 329

7 296 321

8 361 327

9 648 330

10 375 347

11 302 311

12 347 331

13 379 340

14 384 343

15 358 328

16 369 341

17 308 317

18 341 325

19 385 346

20 378 337

(c) the completed 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)	338.5	319.5
Median	364.5	328.5
Upper quartile (Q3)	381.5	338.5
Maximum (Max)
Mean	370.1	328.45
Standard deviation (SD)	69.8	12
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

1. 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 348. 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	370.1	355.1
Median	364.5	359.5

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.