Question

Explain the difference between the following:

1. A population parameter and its point estimate.
2. A population and a corresponding sample mean.
3. Explain in your own words: range, variance and standard deviation for a population.

Answer 1

1. A population parameter summarizes various aspects of the whole population in the form of numerical expressions. It is also known as population characteristics, whereas point estimate of a population parameter is a single value estimate. This single statistic value is considered as the most perfect guess for the parameter value. We can draw inference about population parameter with the help of its point estimate. For example, sample mean or sample proportion is a point estimate of the population mean or population proportion respectively.

2. We always need to select a target population for the purpose of research study. So, the entire set of people or objects having some common characteristics is termed as population. The entire focus of the research study is on the target population which is being selected. For example, population can be people suffering from asthma. Whereas sample mean is the mean of the random sample values that have been taken from the entire population. To calculate sample mean, we can add up the random sample values that have been selected from the population & then divide it by the number of those values.

3. Explanation for range, variance & standard deviation for a population is given below:

Range: We can find the range of a data by subtracting the smallest data value from the largest data value. It is concentrated on only two values of the entire data. It is easy to calculate. So,

Range=Largest Data Value-Smallest Data Value.

For example: We have data values: 14, 18, 20, 15, 12, 11, 8. In this case range will be 20-8=12.

Variance: This statistical measure helps us to know how far the values are spread in a data set from their mean. We can determine the size of the data spread with the help of variance. It is square of standard deviation. So, population variance can be calculated with the help of the following formula:

where,

=population variance

x=individual value

=population mean

N=size of population.

Standard Deviation: This is a measure of dispersion. It helps to measure the dispersal about mean. It is the positive square root of the variance. So, standard deviation for the population can be calculated with the help of the following formula:

where,

=population standard deviation

x=individual value

=population mean

N=size of population.