Question

I 3. The following represent the number of accidents that occurred at seven randomly selected pedestrian crossings in Cape Town in the past year. 3, 7, 2, 3, 5, 9,6 Estimate mean, median, mode, range, the standard deviation and variance of accidents at pedestrian crossings in the whole of Cape Town over the same period.

Answer 1

The no. Of accidents in ascending order is

2,3,3,5,6,7,9

Total 7 events.

Now mean = (2+3+3+5+6+7+9)/7 = 35/7 = 5.

And median is the (n+1)/2 th term (as n is odd)

That is 4th term = 5.

And mode = maximum no. Of times a number occurs (here 3 occurs two time) so, mode = 3.

Now, variance = 1/7 * summation over (xi - mean)^2 = 1/7* [ (2-5)^2 + (3-5)^2 + (3-5)^2 + (5-5)^2 + ( 6-5)^2 + (7-5)^2 + (9-5)^2 ]

= 1/7 * (9+4+4+0+1+4+16) = 38/7 = 5.43

And standard deviation = √variance = √5.43 = 2.33