Question

1. Compare AND contrast the three measures of central tendency: mean, median and mode. List THREE areas of daily life o in which you think one of the mean, median, or mode would be the best choice to describe an “average.” 

2. Discuss the similarities AND differences of the three ways of measuring data variation: (1) range, (2) standard deviation, and (3) box-and-whisker plot.

Answer 1

1. Central tendency use the whole set of data to describe the middle value of the data set.

Mean: we all known that mean is the sum of all observations in a dataset divide by the number of observations. Generally, most of the data sets mean is most appropiate central tendency and it is calculated as

where n is number of observations and x is the random variable values.

The mean can be used both continuous and discrete numerical data but do not used for categorical data.

If data set having some outliers which influenced the distribution, then we cannot use mean.

For this we can use median is the better one option.

Median: is the middle value of data set after arranged the obsevations in ascending or descending order.

It divide the dataset in two parts.If data set having an odd number of observations, the median value is the middle value whereas for an even number of observations, the median value is the mean of the two middle values.

The median value is less effected form outliers but it also not defiend for categorical data

Mode: is the most commonly occurring value in a data set.

The mode has an advantage over the median and the mean as it can be found for both numerical as well as categorical data but may not reflect the central tendency of the distribution very well.

FOr example:

data set of production of wheat for various states ---- mean

number of rooms in 11 hotels in a city ----- median

retirement age --- mode