list of race times: if st. dev. is 22.4, how many times are

please see this standard deviation problem

70, 75, 80, 90, 105, 105, 105, 130, 130, 130.
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

a) One
b)Two
c)Three
d)Four
e)Five

here is what i have :

Average (AVG) = Sum/10 = 102
1 SD below 102" eq to "Below 102-22.4 = 79.6

should i pick numbers greater than 79.6 or less than 79.6 ?

it has been given "more than" in the problem .

Re: standard deviation problem

defeated_soldier said:

please see this standard deviation problem

70, 75, 80, 90, 105, 105, 105, 130, 130, 130.
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times? --- That should answer your question

Click to expand...

Re: standard deviation problem

Yes sir , I already have seen that but there are two key words ...see below

more than 1 standard deviation below the mean of the 10 running times

Now , it becomes confusing.

see this sample distribution graph i found in google


so in our context , i believe we need to find the data in the red strike area because it exactly means more than 1 standard deviation below the mean .


Let me analyze in steps....

in our case we have found mean= 102

SD =22.4

1 standard deviation below the mean =>102-22.4 =79.6

so ,more than 1 standard deviation belowthe mean => more than 79.6

so, i believe we need find numbers more than 79.6



am i correct ?

IF i am wrong , why and where exactly i am wrong.

Re: standard deviation problem

These are confusing statements alright - but generally that is the way these are stated.

In this case, standard interpretation would be "-1 to -oo"

I would pick numbers less than 79.6 (2 numbers in the set)

What does your book say?

Re: standard deviation problem

I would pick numbers less than 79.6 (2 numbers in the set)

Click to expand...

yes...thats correct ...my book also says that.

but the language still confusing me

more than 1 standard deviation below the mean of the 10 running times

I am not able to map the answer with the above language.

whats the point using they keyword "more" ....thats bothering me much