Frequency, f Compare the mean of the raw data with the mean from the grouped fre

Question

Frequency, f

Compare the mean of the raw data with the mean from the grouped frequency distribution. Are they different? Why might they be different?

261 275 236 244 278 296 284 298 289 289 250 256 338 360 341 333 261 268 287 296 313 311 309 309 299 303 277 283 304 305 286 290 286 287 297 299 332 330 309 326 309 326 285 291 295 298 306 315 310 318 318 320 333 321 323 324 327 302 319 Class

Frequency, f

Class Boundaries Class Midpoint, X fX 236-260 4 235.5-260.5 248 992 261-285 9 260.5-285.5 273 2457 286-310 26 285.5-310.5 298 7748 311-335 17 310.5-335.5 323 5491 336-360 3 335.5-360.5 348 1044

Explanation / Answer

mean= (992+2457+7748+5491+1044)/(4+9+26+17+3) = 300.5424

Yes, they are different.

They might be different because the mean of the raw data is calculated directly from raw data, but the mean from the grouped frequency distribution is calculated by the grouped data.

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