Question

Asked Apr 24, 2019

Step 1

**The z-score:**

The *z*-score for a value of the data set, when population mean and standard deviation are unknown, is obtained using the formula:

Step 2

**Calculation of z-scores:**

The given data is first typed into an EXCEL sheet in cells B2:B9 and sorted in ascending order in cells C2:C9.

The *z*-score (rounded to 2 decimal places) for the smallest observation (959) in cell C2 is calculated using the EXCEL formula: **=(B2-AVERAGE(B$2:B$9))/STDEV.S(B$2:B$9)**. It is then dragged till cell C9 to get all the *z*-scores. The following image shows the output:

Step 3

**Quantiles and expected z-scores:**

The quantile for each *z*-score is obtained by first ranking of the observations, starting with 1 for the smallest observation, stored in cells D2:D9. Note that the value 1,072 occurs twice, in 5th and 6th positions. So, the rank for each 1,072 is 5.5.

The quantile for the first rank is obtained in cell E2 using the formula: **=(D2-0.5)/(COUN...**

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