How Do You Calculate Estimated Standard Deviation from Grouped Data?

[Noobnoobnoob]

Ok I've got a maths exam on monday and one of the things that is going to be inside it is standard deviation.
Problem is I don't get it one bit. I tried googling it but I didn't understand any of it.

Could someone explain to me how I would find the estimated standard deviation for the following data please?

Profits (1000s)--------Frequency
-10<x<10------------2
0<x<10---------------5
10<x<20-------------12
20<x<30-------------20
30<50-------------61

The formula is
Square root off (Total (x-mean of x) squared divided by n but I don't get what x and n are.

The estimated mean is 31350
Please help

 

[Tide]

In your sample you have 100 measurements of profit. Each of those 100 measurements represents a value of x which is just a name you are giving to each quantity. Since your measurements are allocated to 5 bins (-10 to 10, 0 to 10 and so on), you do not know the precise value of each of the 100 measurements. One way to handle that would be to assume each measurement is equal to the central value of each bin. For example, you would take two of the measurements to have the value 0 (the middle of the interval -10 to 10).

Use that information to find the mean of all 100 measurements and then use your formula to find the standard deviation.

Incidentally, I think you mistyped your first interval. I am guessing that the interval from -10 to 10 should really be from -10 to 0.

 

[Noobnoobnoob]

In your sample you have 100 measurements of profit. Each of those 100 measurements represents a value of x which is just a name you are giving to each quantity. Since your measurements are allocated to 5 bins (-10 to 10, 0 to 10 and so on), you do not know the precise value of each of the 100 measurements. One way to handle that would be to assume each measurement is equal to the central value of each bin. For example, you would take two of the measurements to have the value 0 (the middle of the interval -10 to 10).

Use that information to find the mean of all 100 measurements and then use your formula to find the standard deviation.

Incidentally, I think you mistyped your first interval. I am guessing that the interval from -10 to 10 should really be from -10 to 0.

Ok you're right about the typo.

So x for the first one would be -5?
So what's N?

 

[HallsofIvy]

Yes, use the middle of each interval. Don't forget to multiply that value by the frequency. "Mean of x" is the sum of those: sum of each interval's center value times its freaquency, divided by 100. And x, of course, is the center value.