Statistics Examples

Find the Standard Deviation of the Frequency Table
Find the midpoint for each group.
Tap for more steps...
The lower limit for every class is the smallest value in that class. On the other hand, the upper limit for every class is the greatest value in that class.
The class midpoint is the lower class limit plus the upper class limit divided by .
Simplify all the midpoint column.
Add the midpoints column to the original table.
Calculate the square of each group midpoint .
Simplify the column.
Multiply each midpoint squared by its frequency .
Simplify the column.
Find the sum of all frequencies. In this case, the sum of all frequencies is .
Find the sum of column. In this case, .
Find the mean .
Tap for more steps...
Find the midpoint for each class.
Multiply the frequency of each class by the class midpoint.
Simplify the column.
Add the values in the column. In this case, .
Add the values in the frequency column. In this case, .
The mean (mu) is the sum of divided by , which is the sum of frequencies.
The mean is the sum of the product of the midpoints and frequencies divided by the total of frequencies. In this case, .
Simplify the right side of to get .
The equation for the standard deviation is .
Substitute the calculated values into to get .
Simplify the right side of to get the variance .
The standard deviation is the square root of the variance . In this case, the standard deviation is .
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]