Eye refractive study. The conventional method of measuring the refractive status of an eye involves three quantities: (1) sphere power, (2) cylinder power, and (3) axis. Optometric researchers studied the variation in these three measures of refraction ( Optometry and Vision Science , June 1995). Twenty-five successive refractive measurements were obtained on the eyes of over 100 university students. The cylinder power measurements for the left eye of one particular student (ID #11) are listed in the table and saved in the LEFTEYE file. [Note : All measurements are negative values.]
.08 | .08 | 1.07 | .09 | .16 | .04 | .07 | .17 | .11 |
.06 | .12 | .17 | .20 | .12 | .17 | .09 | .07 | .16 |
.15 | .16 | .09 | .06 | .10 | .21 | .06 |
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Based on Rubin, A., and Harris, W. F. “Refractive variation during autorefraction: Multivariate distribution of refractive status.” Optometry and Vision Science: Official Publication of the American Academy of Optometry, Vol. 72, No. 6, June 1995, p. 409 (Table).
a. Find measures of central tendency for the data and interpret their values.
b. Note that the data contain one unusually large (negative) cylinder power measurement relative to the other measurements in the data set. Find this measurement. (In Section 2.8, we call this value an outlier).
c. Delete the outlier of part b from the data set and recalculate the measures of central tendency. Which measure is most affected by the deletion of the outlier?
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