6. Following are the speeds (kilometres per hour) at which 20 cars were timed on a highway
in late-evening traffic:
124 111 132 122 111 114 129 106 113 124
116 117 129 138 119 124 111 143 119 121
$\sum x = 2,423$, $\sum x^2 = 295,283$.
(a) Find the mean of these speeds.
(b) If each of the speeds is increased by 20, what would happen to the new mean speed?
Generalize the result.
(c) Find the standard deviation of these speeds.
(d) If each of the speeds is decreased by 15, what would happen to the new standard
deviation speed? Generalize the result.