Example - Sales A large department store collects data on sales made by each of its salespeople. The number of sales made on a given day by each of 20 salespeople is shown on the next slide (see also file sales.sav). Further, the data has been sorted in magnitude. Required: Descriptive Measures.

Example (Continued) - Sales and Sorted Sales Sales Sorted Sales 9 6 6 9 12 10 10 12 13 13 15 14 16 14 14 15 14 16 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24

Example : Finding Quartiles Sorted Sales Sales 9 6 6 9 12 10 10 12 13 13 15 14 16 14 14 15 14 16 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24 (n+1)P/100 Quartiles Position 13 + (.25)(1) = 13.25 (20+1)25/100=5.25 First Quartile (20+1)50/100=10.5 16 + (.5)(0) = 16 Median (20+1)75/100=15.75 18+ (.75)(1) = 18.75 Third Quartile

Example – Median (Data is used from Example ) Sales Sorted Sales 9 6 6 9 12 10 10 12 13 13 15 14 16 14 14 15 14 16 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24 Median 50th Percentile (20+1)50/100=10.5 16 + (.5)(0) = 16 Median The median is the middle value of data sorted in order of magnitude. It is the 50th percentile.

Example - Mode (Data is used from Example ) . . . . . . : . : : : . . . . . --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24 Mode = 16 The mode is the most frequently occurring value. It is the value with the highest frequency.

Example – Mean (Data is used from Example) Sales 9 6 12 10 13 15 16 14 17 24 21 22 18 19 20 317 x n i = å 1 317 20 15 85 .

Example - Range and Interquartile Range (Data is used from Example) Sorted Sales Sales Rank 9 6 1 6 9 2 12 10 3 10 12 4 13 13 5 15 14 6 16 14 7 14 15 8 14 16 9 16 16 10 17 16 11 16 17 12 24 17 13 21 18 14 22 18 15 18 19 16 19 20 17 18 21 18 20 22 19 17 24 20 Range: Maximum - Minimum = 24 - 6 = 18 Minimum Q1 = 13 + (.25)(1) = 13.25 First Quartile Q3 = 18+ (.75)(1) = 18.75 Third Quartile Interquartile Range: Q3 - Q1 = 18.75 - 13.25 = 5.5 Maximum

Calculation of Sample Variance 6 -9.85 97.0225 36 9 -6.85 46.9225 81 10 -5.85 34.2225 100 12 -3.85 14.8225 144 13 -2.85 8.1225 169 14 -1.85 3.4225 196 14 -1.85 3.4225 196 15 -0.85 0.7225 225 16 0.15 0.0225 256 17 1.15 1.3225 289 17 1.15 1.3225 289 18 2.15 4.6225 324 19 3.15 9.9225 361 20 4.15 17.2225 400 21 5.15 26.5225 441 22 6.15 37.8225 484 24 8.15 66.4225 576 317 0 378.5500 5403