Question

Which measure of central tendency would you use for the following variables (mean, median or mode). Explain your choice.

Gender: _______________________________________________________

Class rank at a college: __________________________________________________

Age of high school students: ________________________________________

A skewed income distribution (90% with incomes under $150K; a few with incomes of several million): ____________________________________________________

Which measure of central tendency would you use for the following variables (mean, median or mode). Explain your choice.

Gender: _______________________________________________________

Class rank at a college: __________________________________________________

Age of high school students: ________________________________________

A skewed income distribution (90% with incomes under $150K; a few with incomes of several million): ____________________________________________________

Answer 1

Gender : Mode

Type of data for gender is qualitative data. So we can't use mean as measure of central tendency but we can use median or mode . Now median is more appropriate when we can put data in certain order and find it's center . But in case of gender ordering is not possible but the gender which occurs more frequently can be said as average . Therefore Mode is appropriate measure .

Class rank at the college : Median

Class rank is qualitative type of data. ( Even though it is a number it is just a attribute and not a measurement or count of Variable ) . We can arrange the data in ascending order and hence median is appropriate measure of central tendency.

Age of high school students : Mean

Age is quantitative data and hence Mean is appropriate measure of central tendency . For ratio scale data Usually mean is used as measure of central tendency .

Skewed income distribution : Median

Whenever distribution is skewed Median is best measure of central tendency for interval or ratio scale data. Mean is not appropriate since it will get affected by extreme values in dataset.

Further questions are repetition.