standard deviation

[akredd90]

The list shown consists of the times, in seconds,that it took each of 10 school children to run a distance of 400 meters. If the standard deviation of the running times is 22.4,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?
70,75,80,85,90,105,105,130,130,130


A) One
B) Two
C) three
D) four
E) five

[shubham_sagijain]

The list shown consists of the times, in seconds,that it took each of 10 school children to run a distance of 400 meters. If the standard deviation of the running times is 22.4,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

Where is the list ? Please post the list as well.

Thanks,
Shubh

[akredd90]

The list shown consists of the times, in seconds,that it took each of 10 school children to run a distance of 400 meters. If the standard deviation of the running times is 22.4,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

Where is the list ? Please post the list as well.

Thanks,
Shubh

Sorry .
I added the list in the question above.

Thank you

[shubham_sagijain]

The list shown consists of the times, in seconds,that it took each of 10 school children to run a distance of 400 meters. If the standard deviation of the running times is 22.4,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

1) Calculate the mean of the given list
2) Subtract 1 S.D i.e 22.4 from the mean.
3) Now, notice that you will have only 2 values (running times) that are 'more than 1 SD below the mean'

Thanks,
Shubh

[jnelson0612]

Thanks Shubh! Nice concise explanation. :-)

[baladon99]

Although the method explained is perfectly alright, I feel the answer is 3.
Mean =100
S.D =22.4
mean-One S.D =77.6

Between 77.6 and 100 there are three values --> 80 , 85 and 90.

[RonPurewal]

baladon99, i see what you're doing there, but that's not how the language works in this particular instance.

when you see "more than X amount below Y", the correct interpretation of this statement is "below Y by more than X amount". in other words, less than the quantity (Y - X).

i see how you got your interpretation -- you read the statement as "greater than a number that is one standard deviation below the mean" -- but, in this instance, that's an incorrect interpretation.

[baladon99]

baladon99, i see what you're doing there, but that's not how the language works in this particular instance.

when you see "more than X amount below Y", the correct interpretation of this statement is "below Y by more than X amount". in other words, less than the quantity (Y - X).

i see how you got your interpretation -- you read the statement as "greater than a number that is one standard deviation below the mean" -- but, in this instance, that's an incorrect interpretation.

Thanks Ron. Guess I have understood the right interpretation now.
If the question is ,
how many of the 10 running times are more than 1 standard deviation above the mean of the 10 running times?

Will the answer be 3 ? i.e. 130 , 130 and 130.

Thanks ,

Bala

[tanyatomar]

Hey Bala :) i think it should be 2 values (75 and 70) -->> mean is 110.
therefore 22.4 reduced from 110 = 77.6. Now only 2 values (75 n 70 are below 77.6...
:) let me know if am wrong :)

[jnelson0612]

baladon99, i see what you're doing there, but that's not how the language works in this particular instance.

when you see "more than X amount below Y", the correct interpretation of this statement is "below Y by more than X amount". in other words, less than the quantity (Y - X).

i see how you got your interpretation -- you read the statement as "greater than a number that is one standard deviation below the mean" -- but, in this instance, that's an incorrect interpretation.

Thanks Ron. Guess I have understood the right interpretation now.
If the question is ,
how many of the 10 running times are more than 1 standard deviation above the mean of the 10 running times?

Will the answer be 3 ? i.e. 130 , 130 and 130.

Thanks ,

Bala

Correct! If one standard deviation above the mean is 122.4, then three points (130, 130, 130) are more than one standard deviation above the mean.

[jnelson0612]

Hey Bala :) i think it should be 2 values (75 and 70) -->> mean is 110.
therefore 22.4 reduced from 110 = 77.6. Now only 2 values (75 n 70 are below 77.6...
:) let me know if am wrong :)

I calculated the mean at 100 . . . can you check your math again?

[krishnan.anju1987]

Same here, even I calculated the mean as 100 and the value below which running times are to be found as 79.6.. That's right isn't it?

[jnelson0612]

Same here, even I calculated the mean as 100 and the value below which running times are to be found as 79.6.. That's right isn't it?

We agree on the mean as 100 and that is good. :-)

However, if the standard deviation is 22.4, then one standard deviation below the mean would be 100-22.4 = 77.6. That is the value corresponding with one standard deviation below the mean. We would then ask ourselves how many data points in this list are below 77.6. I see 70 and 75, or two data points.

[krishnan.anju1987]

Yup, that was my mistake and now that I look at the numbers again, pretty obvious one at that.

[jnelson0612]

Yup, that was my mistake and now that I look at the numbers again, pretty obvious one at that.

Glad that things are all cleared up! :-)