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Mean square

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355: 218: 261: 108: 132: 396: 420: 389: 48: 296: 230: 62: 224: 123: 86: 8: 382: 276: 72: 370: 324: 36: 272: 32: 80: 40: 28: 415: 366: 119: 409: 213:{\displaystyle s^{2}=\textstyle {\frac {1}{n-1}}\sum (x_{i}-{\bar {x}})^{2}} 57: 362: 268: 20: 67: 46:
It may also be defined as the arithmetic mean of the squares of the
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between a set of numbers and a reference value (e.g., may be a
279:
of a random variable when the random variable is zero-mean.
53: 149: 122:, and this is still called the "mean square" (e.g. in 233: 135: 89: 275:(RMS or rms), and can be used as an estimate of the 255: 212: 110:uses a divisor of the number of values minus one, 102: 407: 304:engineering.purdue.edu/ME365/Textbook/chapter11 60:of the data), in which case it may be known as 390: 397: 383: 66:. When the reference value is the assumed 408: 16:Average of squared values of a sample 349: 325:"OECD Glossary of Statistical Terms" 13: 14: 432: 271:of a mean square is known as the 353: 317: 289: 250: 237: 200: 193: 171: 1: 282: 369:. You can help Knowledge by 83:from a set of sample values 7: 297:"Noise and Noise Rejection" 79:A typical estimate for the 27:is normally defined as the 10: 437: 348: 23:and its applications, the 70:, the result is known as 256:{\displaystyle E(X^{2})} 365:-related article is a 257: 227:of a random variable, 214: 104: 258: 215: 105: 103:{\displaystyle x_{i}} 63:mean square deviation 231: 133: 124:analysis of variance 87: 263:is also called the 39:of numbers or of a 277:standard deviation 253: 210: 209: 100: 73:mean squared error 421:Mathematics stubs 378: 377: 196: 166: 428: 399: 392: 385: 357: 350: 340: 339: 337: 335: 321: 315: 314: 312: 310: 301: 293: 273:root mean square 262: 260: 259: 254: 249: 248: 219: 217: 216: 211: 208: 207: 198: 197: 189: 183: 182: 167: 165: 151: 145: 144: 109: 107: 106: 101: 99: 98: 436: 435: 431: 430: 429: 427: 426: 425: 406: 405: 404: 403: 346: 344: 343: 333: 331: 323: 322: 318: 308: 306: 299: 295: 294: 290: 285: 244: 240: 232: 229: 228: 203: 199: 188: 187: 178: 174: 155: 150: 140: 136: 134: 131: 130: 118:as in a simple 94: 90: 88: 85: 84: 81:sample variance 41:random variable 29:arithmetic mean 17: 12: 11: 5: 434: 424: 423: 418: 402: 401: 394: 387: 379: 376: 375: 358: 342: 341: 316: 287: 286: 284: 281: 252: 247: 243: 239: 236: 221: 220: 206: 202: 195: 192: 186: 181: 177: 173: 170: 164: 161: 158: 154: 148: 143: 139: 120:quadratic mean 114:, rather than 97: 93: 15: 9: 6: 4: 3: 2: 433: 422: 419: 417: 414: 413: 411: 400: 395: 393: 388: 386: 381: 380: 374: 372: 368: 364: 359: 356: 352: 351: 347: 330: 326: 320: 305: 298: 292: 288: 280: 278: 274: 270: 266: 245: 241: 234: 226: 204: 190: 184: 179: 175: 168: 162: 159: 156: 152: 146: 141: 137: 129: 128: 127: 125: 121: 117: 113: 95: 91: 82: 77: 75: 74: 69: 65: 64: 59: 55: 51: 50: 44: 42: 38: 34: 30: 26: 22: 371:expanding it 360: 345: 332:. Retrieved 328: 319: 307:. Retrieved 303: 291: 264: 222: 115: 111: 78: 71: 61: 58:assumed mean 47: 45: 24: 18: 363:mathematics 269:square root 265:mean square 223:The second 25:mean square 21:mathematics 410:Categories 283:References 68:true value 49:deviations 334:6 January 309:6 January 194:¯ 185:− 169:∑ 160:− 329:oecd.org 33:squares 31:of the 267:. The 225:moment 56:or an 416:Means 361:This 300:(PDF) 35:of a 367:stub 336:2020 311:2020 54:mean 126:): 112:n-1 43:. 37:set 19:In 412:: 327:. 302:. 76:. 398:e 391:t 384:v 373:. 338:. 313:. 251:) 246:2 242:X 238:( 235:E 205:2 201:) 191:x 180:i 176:x 172:( 163:1 157:n 153:1 147:= 142:2 138:s 116:n 96:i 92:x

Index

mathematics
arithmetic mean
squares
set
random variable
deviations
mean
assumed mean
mean square deviation
true value
mean squared error
sample variance
quadratic mean
analysis of variance
moment
square root
root mean square
standard deviation
"Noise and Noise Rejection"
"OECD Glossary of Statistical Terms"
Stub icon
mathematics
stub
expanding it
v
t
e
Categories
Means
Mathematics stubs

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