Question

1. for each of the datasets described below, decide which measure of central tendency would be most appropriate and explain your choice. consider thescale of measurement for each variable and the likely distribution of the observations.

a. the scores of 500 grade 6 students on a nationwide standardized math test
b. the type of car chosen by 120 new car buyers.
c. the salaries of all employees (including executives and ceo) of a large company.
d. which average is defined as the value that has 50% of the cases below it?

Explanation:

a.

The scores of students on a standardized test are likely to follow a normal - like distribution. The mean is appropriate as the data is numerical and on an interval/ratio scale, and the mean takes into account all values in the dataset.

b.

The type of car is a categorical variable. The mode is the most appropriate measure as it represents the most frequently occurring category.

c.

Salaries often have a skewed distribution due to high - earning executives and CEOs. The median is a better measure as it is not affected by extreme values.

d.

The value that has 50% of the cases below it is the median. It divides the data set into two equal halves.

Answer:

a.

Mean; data is numerical, interval/ratio scale and likely normal - like distribution.

b.

Mode; data is categorical.

c.

Median; data is likely skewed due to extreme values.

d.

Median.