Chebyshev came up with the
limits on how much or how many of the data must lie close to the mean. In specific
for any positive k, the proportion of the data that lies within k standard
deviations of the mean is at least: <span>
1 - 1/k²
<span>In this problem the
mean is 47 yrs therefore:
(47 – 17.3) = 29.7 = (76.7 - 47) </span></span>
The value of k is
calculated using the formula:<span>
29.7 / 11 = 2.7 = k</span>
So the % of gym members
aged between 19.4 and 76.6 is: <span>
1 - 1 / (2.6)² = 0.863 = 86.3 %</span>
<span>Therefore 86.3% of the
gym members are aged between 19.4 and 76.6</span>
