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By Irving W. Burr and J. William Schmidt (Auth.)

ISBN-10: 0121461505

ISBN-13: 9780121461508

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In the attempt to obtain more reliable values some statisticians use the so-called ^-statistics, which take into account the sample size, rather than using the m^s directly. Thus s2 is the second ^-statistic. But the use of ^-statistics is essentially a correction to the mi values, dependent on n, and for large n's such as we should have to justify calculating a3 and #4 , the correction is quite slight. Hence we ignore it. 6. SUMMARY In this chapter we have been concerned with several objective measures for summarizing sample data, either discrete or continuous.

This does not tell us much, especially since in all cases YXy ~~ y) = 0 (except for round-off errors). Hence we must do something else to find a typical deviation from the mean. One solution is to neglect signs, and sum the absolute deviations | y — y |, then divide by n. This gives the "mean deviation'' y Iy _ yI mean deviation = —. 3. 32 cc , . 464 cc. Note that three of the deviations | y — y | exceed this value, and two are less. '' For it we square all of the deviations as in the last column of the table, and add.

3. 32 cc , . 464 cc. Note that three of the deviations | y — y | exceed this value, and two are less. '' For it we square all of the deviations as in the last column of the table, and add. 3280 cc2, by n = 5. Indeed, this used to be the common practice. However, for certain theoretical reasons, which appear in Chapter 7, the present practice is to divide X(V ~ y)2 by n — I instead of n. This gives what is called the "sample variance," its symbol being s2. sample variance = s2 = V (y _ y)2 —^— .

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