The coaches of a local football team wanted to determine whether the players on their team were older than those of others teams. they recorded the ages of the players on two of the teams as follows:
team a: 25, 25, 28, 30, 25, 25, 24, 25, 22, 21, 19,
20, 22, 33, 28, 25, 26, 30, 28, 22, 24, 21
team b: 23, 23, 26, 27, 24, 20, 21, 23, 25, 21, 22,
29, 28, 29, 28, 27, 23, 23, 26, 32, 23, 20
a set of descriptive statistics was computed for both teams’ ages, along with adjacent five number summaries below.
team a team b
mean 24.909 mean 24.682
standard error 0.756 standard error 0.694
median 25 median 23.5
mode 25 mode 23
standard deviation 3.544 standard deviation 3.257
sample variance 12.563 sample variance 10.608
kurtosis -0.112 kurtosis -0.496
skewness skewness
range 14 range 12
minimum 19 minimum 20
maximum 33 maximum 32
sum 548 sum 543
count 22 count 22
confidence level 1.571 confidence level 1.444
(95.0%) (95.0%)
five-number summary
team a team b
minimum 19 20
first quartile 22 23
median 25 23.5
third quartile 28 27
maximum 33 32
1. given one of the aims of this analysis is to make inferences about the average age of all football players (there are 16 teams in the competition), what type of sampling scheme has been used here? briefly explain.
2. for which team, team a or team b, is age more variable? refer to and/or compute two different statistics to support your answer.
3. by using either descriptive statistics, comment on the skewness of both teams’ age distributions.