Question

1. A survey administered to a random sample from a local grocery store finds that political party is related to whether or not they favor an increase in sales tax, leading to a news story: Republicans support proposed tax increase. This is an example of what type of statistic?

2. What are measures of central tendency? When is each appropriate? What influences each measure of central tendency? (ex. What is affected by every score in the distribution? If you change only the highest score, what measure does that change?). What is the preferred measure of central tendency for a skewed variable? What is the purpose of measures of central tendency?

Answer 1

Solution:-

1. Here, given that  a survey administered to a random sample from a local grocery store finds that political party is related to whether or not they favor an increase in sales tax, leading to a news story: Republicans support proposed tax increase. This is an example of inferential statistic. Since, the statistic involves here, infers about the properties of the population.

2. The measures of central tendency are: Mean, Median, and Mode.

Each of them are appropriate in the following cases:

Suitable Cases (Measurement scale):	Best measures of Central tendency
Nominal (Categorical)	Mode
Ordinal	Median
Interval	Symmetrical data : Mean Skewed data : Median
Ratio	Symmetrical data : Mean Skewed data : Median

All the measures of the central tendency (such as, Mean, Median & Mode) are affected by every score of the distribution.

The things which influence each measure of central tendency are:-

Mean:- It takes into account all the values, to calculate the average. The simplest measure among all the other members of central tendency.

Median :- This measure is very important, as it does not get affected by the large values or very small values. It helps in case of the presence of outliers in the data and if the data is skewed.

Mode :- This measure of central tendency can be used, when the data set is not in numbers.

Median is the preferred measure of central tendency for a skewed variable.

The purpose of measures of central tendency is that they provide a single value, which is used to describe a set of data by identifying the central position within that set of data. They are sometimes called as the measures of central location. They gives us roughly the small summary of the data set. We can think of the tendency of the data, that it cluster around the middle or the center point. Mean, Median and Mode are the common measure of central tendency where each of these measures calculates the location of the central point using a different method.