Please tell me if my answers are right.
Suppose that a series of measurements have shown that the mean mass of an object is 122.4g with a standard deviation of 1.3g. How many significant figures are justified in the mean and how would you report the most probably mass of the object?
a.)Number of significant figures justified in mean value:
b.) Most probable mass of the object:
for a I got 3
for b I got 94.2
a) Correct.
b) What. How did you even?
It is 122±2g
To determine the number of significant figures justified in the mean value, you need to consider the least precise measurement used to calculate the mean. In this case, the least precise measurement is given by the standard deviation, which has two significant figures (1.3g). Therefore, the number of significant figures justified in the mean value is also two.
Regarding the most probable mass of the object, it is not clear how you arrived at the value of 94.2g. However, you can determine the most probable mass by using the mean value of 122.4g as it represents the average of the measured masses. Therefore, the most probable mass of the object is 122.4g, rounded to the same number of significant figures justified in the mean value (two significant figures).
To determine the number of significant figures justified in the mean value, you can look at the precision of the measurements given. In this case, the standard deviation of the measurements is given as 1.3g. Typically, the number of significant figures in a calculated value should match the number of significant figures in the least precise measurement used in the calculation.
In this case, the mean mass is reported as 122.4g, which has four significant figures. Since the standard deviation has two significant figures (1.3g), the least precise measurement only has two significant figures. Therefore, the number of significant figures justified in the mean value would be two.
So the answer for part a) is 2.
Now, let's move on to part b) - the most probable mass of the object.
Considering the mean mass reported as 122.4g, the significant figures in the mean determine the precision. Since the mean has four significant figures, we can report the most probable mass of the object as 122.4g.
Thus, the answer for part b) is 122.4g.