In the Assumed Mean Method, if the assumed mean $A=55$ and an observed value $x=40$, what is the deviation $d$?

The correct option is -15.

Step-by-step Explanation:

In statistics, when calculating the mean of a grouped or ungrouped data set using the Assumed Mean Method, we define a deviation for each observed value from a chosen assumed mean.

The deviation, denoted by $d$, is calculated as the difference between the observed value ($x$) and the assumed mean ($A$). The formula to find the deviation is:
$d=x-A$

From the given problem, we have the following values:
Assumed mean, $A=55$
Observed value, $x=40$

Substituting these values into the deviation formula, we get:
$d=40-55$
$d=-15$

Since the observed value is less than the assumed mean, the resulting deviation is negative. Therefore, the deviation is $-15$.