Question

answer the questions below:
(a) the 9 members of a fraternity have the following test scores:
118, 119, 122, 123, 124, 127, 128, 129, 131.
which measure should be used to summarize the data?
o mean
o median
o mode
(b) in a survey, 9 people reported how many soft drinks they drank in the last month. here are their
responses:
8, 28, 29, 30, 33, 35, 36, 37, 39.
which measure should be used to summarize the data?
o mean
o median
o mode
(c) the readers of a childrens magazine are asked to name their favorite animals.
which measure indicates the animal chosen most often?
o mean
o median
o mode

Explanation:

(a)

Step1: Analyze data type and measure suitability

The data is test scores (numerical, no outliers). Mean is good for symmetric data. Let's check symmetry. First, order the data: 118, 119, 122, 123, 124, 127, 128, 129, 131. The data is roughly symmetric. Mean is appropriate as it uses all values.

Step2: Check other measures

Median is middle value, but mean is better for symmetric numerical data without outliers. Mode: all values unique, so mode not useful.

Step1: Analyze data (outlier)

Data: 8, 28, 29, 30, 33, 35, 36, 37, 39. The value 8 is an outlier. Median is resistant to outliers, so better for data with outliers.

Step2: Compare measures

Mean is affected by outlier (8 would lower mean). Mode: all values unique. So median is best.

Step1: Data type (categorical)

Favorite animals are categories (e.g., dog, cat). Mode is the most frequent category, suitable for categorical data.

Step2: Other measures

Mean and median don't apply to categorical data. So mode is best.

Answer:

Mean

(b)