The standard deviation is the maximum and the minimum variation in the data set from the mean. The value of the standard deviation is 1.5.
The standard deviation is the maximum and the minimum variation in the data set from the mean.
Given that the mean shoe size is 7.5, while the size of shoe for the entire class is only 1 deviation, and the value is 6 and 9. Therefore, the equation of the standard deviation and the mean can be written as,
[tex]\mu -\sigma < x < \mu +\sigma \\6 < x < 9[/tex]
Now, the value of the standard deviation can be written as,
[tex]\mu - \sigma = 6\\\\-\sigma = 6-7.5\\\\-\sigma = -1.5\\\\\sigma = 1.5[/tex]
or the value of the standard deviation can be written as,
[tex]\mu + \sigma = 9\\\\ \sigma = 9-7.5\\\\ \sigma = 1.5[/tex]
Hence, the value of the standard deviation is 1.5.
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