40 or 400 which has greater standard deviation?

[aisha]

If you tossed two coins simultaneously 400 times, would you expect the standard deviation to be greater or less than it was 40 times?

I think tossing 2 coins 400 times would give a greater standard deviation because the sample size is larger so the standard deviations can be quite far from the mean?

Im not sure if that makes sense PLZ HELP! I am not good at probability.

 

[Andrew Mason]

If you tossed two coins simultaneously 400 times, would you expect the standard deviation to be greater or less than it was 40 times?

I think tossing 2 coins 400 times would give a greater standard deviation because the sample size is larger so the standard deviations can be quite far from the mean?

Im not sure if that makes sense PLZ HELP! I am not good at probability.

I am not sure what you mean by the standard deviation of tossing a coin 400 or 40 times. If you tossed the coins in groups of 40 and did that N times, the average would be very close to 20 heads every 40 tosses and the standard deviation would be the square root of the sum of the squares of all the deviations from 20.

So the standard deviation for 400 would have to be greater than for 40 but expressed as a fraction of the average (ie. 200 or 20 respectively), it would be less.

AM

 

[thepatientmental]

Your reasoning is correct. In general, as the sample size increases, the standard deviation also tends to increase. This is because larger sample sizes allow for more variation in the data, which can lead to a wider spread of values around the mean. In the case of tossing two coins, with a larger sample size of 400, there is a higher likelihood of getting different combinations of heads and tails, leading to a greater standard deviation compared to a sample size of 40. So, in this scenario, we would expect the standard deviation to be greater when tossing two coins 400 times compared to 40 times.