Problem Solving

Numbers given: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the time it took each of 10 schoolchildren to run a distance of 400 meters. If the Standard Deviation (SD) of 10 running times is 22.4 seconds. How many of the 10 running times are more than 1 SD below the mean of 10 running times?

1) 1
2) 2
3) 3
4) 4
5) 5


[spoiler]OA is 2)[/spoiler]

1. Find the Mean:

Add the Numbers given: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130 = 1000
Mean = 1000 / 10 = 100.

2. Find 1SD below the mean.

100 - 22.4 = 77.6

3. Locate the numbers those are more than 1 SD below the mean.
(this is a tricky part, numbers have MORE than 1 SD below the MEAN means we have to find the numbers those are LESS than 77.6 .
The reason we find less is if we were asked to find the 2SD below mean then it would have been Mean - 2SD which would be 55.2 .
55.2 is More than 1SD below the mean because 55.2 is 2SD below the mean )

70 and 75 are less than 77.6

Thus IMO B

Mean= 100

One std dev below the mean = 100 - 22.4 = 77.6

Ans : 2

Thanks Shovan,

If we are asked to find 2SD below mean, than also we would find numbers < (Mean - 2SD)?

Yes, B is the correct answer.

If we are asked to find 2SD below mean, than also we would find numbers < (Mean - 2SD)?

You're right.