Let's address each part of the question step-by-step:
### Part (a)
Question:
Each member of the football team was asked to report the year he was born. Which measure gives the most common year of birth?
Answer:
To identify the most common year of birth among the football team members, we use the Mode. The mode is the statistical measure that represents the value that appears most frequently in a data set. In this case, it will tell us the year that the highest number of team members were born.
Answer: Mode
### Part (b)
Question:
A car dealer has used cars for sale for the following amounts:
[tex]$1100, $[/tex]3400, [tex]$3500, $[/tex]3600, [tex]$3700, $[/tex]3800, [tex]$3900, $[/tex]4100, $4200.
Which measure should be used to summarize the data?
Answer:
When summarizing car prices where there might be extreme values (potential outliers), the Median is preferred. The median is the middle value of a data set when it is ordered from least to greatest. It provides a better central tendency measure because it is not affected by extremely high or low values, unlike the mean.
Answer: Median
### Part (c)
Question:
In a survey, 9 people gave the following ratings for a local politician (on a scale of 0 to 100):
40, 42, 43, 44, 49, 51, 52, 54, 55.
Which measure should be used to summarize the data?
Answer:
To summarize the ratings, the Median should be used. The median gives the middle rating, providing a central tendency that is not influenced by the potential extremes in the data. The median is especially useful for ordinal data or skewed distributions to provide a central point.
Answer: Median
Therefore, the recommended measures for each part of the question are:
(a) Mode
(b) Median
(c) Median
