Question

The ABC company is planning to analyze the average weekly wage distribution of its 58 employees during fiscal year 2003. The 58 weekly wages are available as raw data corresponding to the alphabetic order of the employees names: 241 253 312258264 265 316 242 257251282305 298276 284 304285 307 263 301 262272 271 265 249 229 253 285267250 288 248 276 280 252258 262 314 241 257 250 275 275 301 283 249 288 275 281 276 289 228 275 170 289 262 282 260 (6 points) a. Calculate the mean, median, and mode of the data. b. Calculate the standard deviation, skewness, and kurtosis of the data.(9 points) c. Construct a frequency distribution for the data. d. Draw a histogram for the frequency distribution in part c (5 points) (10 points)Please type your answer. Thanks!

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Answer #1

SoluttionA:

mean=sum of values/total values=15651/58= 269.8448

median is middle most value after data is sorted:

170 228 229 241 241 242 248 249 249 250 250 251 252 253 253 257 257
258 258 260 262 262 262 263 264 265 265 267 271 272 275 275 275 275
276 276 276 280 281 282 282 283 284 285 285 288 288 289 289 298 301
301 304 305 307 312 314 316

median=271+272/2=271.5

mode=275 as it repeats 4 times

Solutionb:

wages(X) xbar x-xbar (x-xbar)^2 (x-xbar)^3 (x-xbar)^4
241 269.8448 -28.8448 832.0225 -23999.5 692261.4
253 269.8448 -16.8448 283.7473 -4779.67 80512.52
312 269.8448 42.1552 1777.061 74912.36 3157945
258 269.8448 -11.8448 140.2993 -1661.82 19683.89
264 269.8448 -5.8448 34.16169 -199.668 1167.021
265 269.8448 -4.8448 23.47209 -113.718 550.9389
316 269.8448 46.1552 2130.302 98324.54 4538189
242 269.8448 -27.8448 775.3329 -21589 601141.1
257 269.8448 -12.8448 164.9889 -2119.25 27221.33
251 269.8448 -18.8448 355.1265 -6692.29 126114.8
282 269.8448 12.1552 147.7489 1795.917 21829.73
305 269.8448 35.1552 1235.888 43447.89 1527419
298 269.8448 28.1552 792.7153 22319.06 628397.5
276 269.8448 6.1552 37.88649 233.1989 1435.386
284 269.8448 14.1552 200.3697 2836.273 40148.01
304 269.8448 34.1552 1166.578 39844.69 1360903
285 269.8448 15.1552 229.6801 3480.848 52752.94
307 269.8448 37.1552 1380.509 51293.08 1905805
263 269.8448 -6.8448 46.85129 -320.688 2195.043
301 269.8448 31.1552 970.6465 30240.69 942154.6
262 269.8448 -7.8448 61.54089 -482.776 3787.281
272 269.8448 2.1552 4.644887 10.01066 21.57498
271 269.8448 1.1552 1.334487 1.541599 1.780856
265 269.8448 -4.8448 23.47209 -113.718 550.9389
249 269.8448 -20.8448 434.5057 -9057.18 188795.2
229 269.8448 -40.8448 1668.298 -68141.3 2783217
253 269.8448 -16.8448 283.7473 -4779.67 80512.52
285 269.8448 15.1552 229.6801 3480.848 52752.94
267 269.8448 -2.8448 8.092887 -23.0226 65.49482
250 269.8448 -19.8448 393.8161 -7815.2 155091.1
288 269.8448 18.1552 329.6113 5984.159 108643.6
248 269.8448 -21.8448 477.1953 -10424.2 227715.3
276 269.8448 6.1552 37.88649 233.1989 1435.386
280 269.8448 10.1552 103.1281 1047.286 10635.4
252 269.8448 -17.8448 318.4369 -5682.44 101402.1
258 269.8448 -11.8448 140.2993 -1661.82 19683.89
262 269.8448 -7.8448 61.54089 -482.776 3787.281
314 269.8448 44.1552 1949.682 86088.58 3801259
241 269.8448 -28.8448 832.0225 -23999.5 692261.4
257 269.8448 -12.8448 164.9889 -2119.25 27221.33
250 269.8448 -19.8448 393.8161 -7815.2 155091.1
275 269.8448 5.1552 26.57609 137.005 706.2884
275 269.8448 5.1552 26.57609 137.005 706.2884
301 269.8448 31.1552 970.6465 30240.69 942154.6
283 269.8448 13.1552 173.0593 2276.63 29949.52
249 269.8448 -20.8448 434.5057 -9057.18 188795.2
288 269.8448 18.1552 329.6113 5984.159 108643.6
275 269.8448 5.1552 26.57609 137.005 706.2884
281 269.8448 11.1552 124.4385 1388.136 15484.94
276 269.8448 6.1552 37.88649 233.1989 1435.386
289 269.8448 19.1552 366.9217 7028.458 134631.5
228 269.8448 -41.8448 1750.987 -73269.7 3065956
275 269.8448 5.1552 26.57609 137.005 706.2884
170 269.8448 -99.8448 9968.984 -995351 99380644
289 269.8448 19.1552 366.9217 7028.458 134631.5
262 269.8448 -7.8448 61.54089 -482.776 3787.281
282 269.8448 12.1552 147.7489 1795.917 21829.73
260 269.8448 -9.8448 96.92009 -954.159 9393.503
total 35579.6 -761091 1.28E+08
samplestandarddeviation=s=sqrt(35579.6/58-1)
samplesd=s=24.98407

skewness=

(2.-.rbar))3/(n-1)ơ3=-761091/(58-1)*24.9841^3

skewness=-0.8562

kurtossis=sum (x-xbar))^4/(n-1)sigma ^4

=5.7716

=

Soutionc:

class Frequency
170-193 1
193-216 0
216-239 2
239-262 20
262-285 22
285-308 10
308-331 3

Solutiond:

class 170-193 193-216 216-239 239-262 262-285 285-308 308-331 25 Frequency 20 20 20 15 10 10 10 3 0 [170, 193] (193, 216 (216, 239] 239, 262](262, 285] (285, 308] (308, 331]

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