Question

1. for these situations, state which measure of central tendency—mean, median, or mode—should be used.

a. the most typical case is desired.
b. the distribution is open - ended.
c. there is an extreme value in the data set.
d. the data are categorical.
e. further statistical computations will be needed.
f. the values are to be divided into two approximately equal groups, one group containing the larger values and one containing the smaller values.

Explanation:

a. The mode represents the most frequently occurring value, so it is best for finding the most typical case.
b. The median is robust to open - ended distributions as it only depends on the middle value(s) after ordering the data.
c. The median is not affected by extreme values, while the mean is. So, median is preferred when there are extreme values.
d. For categorical data, the mode is the appropriate measure as we are looking for the most common category.
e. The mean is used when further statistical computations are needed as it has nice mathematical properties for calculations like variance and standard deviation.
f. The median divides the data into two approximately equal groups, one with larger values and one with smaller values.

Answer:

a. Mode
b. Median
c. Median
d. Mode
e. Mean
f. Median