Question

Arithmetic mean for ungrouped data can be calculated by ________.

• A. assumed mean method
• B. direct method
• C. step deviation method
• D. all of the above

Answer 1

Answer: (D)

all of the above

The mean of the data set can be found in various ways:

Firstly, we can use the direct method which involves using the formula $\overline{X}=\frac{\sum X}{N}$

Secondly, we can use the assumed mean method, this is usually used when the number of observations is too large to use the direct method. Here, the mean is assumed on the basis of logic and or general observation. This is usually the centrally located value in the data set. The calculate the deviation of all values from the mean, add up all the deviations and divide this sum by the number of observations, and add this value to the assumed mean.

$\overline{X}=A+\frac{\sum d}{N}$

The step deviation method can be used in conjunction to the assumed mean method. We carry out all the steps of the assumed mean with a slight addition. If it is found that the deviations, (X-A) are too large we can choose to divide all deviations by a common factor c. Thus we use the formula:

$d^{\prime }=\frac{X_i-A}{c}$

$\overline{X}=A+\frac{\sum d^{\prime }}{N}\times c$