Question

11. The table below describes a sample of 15 players in Major League Baseball, chosen from the starting lineups of teams in 2019. The table shows the team, age, position, height, and salary for each player, as well as several statistics from that season. These include the number of games they played (G), their batting average (AVE) (the proportion of their at-bats for which they got a hit), and their home runs (HR). Name Team Age Height G AVE HR Salary Cedric Mullins Orioles 25 173 cm 22 .094 0 $557,500 Tim Anderson White Sox 26 185 cm 123 .335 18 $1,400,000 Christin Stewart Tigers 25 183 cm 104 .233 10 $556,400 Alex Gordon Royals 35 185 cm 150 .266 13 $20,000,000 Jonathan Schoop Twins 27 185 cm 121 .256 23 $7,500,000 Marcus Semien Athletics 29 183 cm 162 .285 33 $5,900,000 Yandy Diaz Rays 28 188 cm 79 .267 14 $558,400 Randal Grichuk Blue Jays 28 188 cm 151 .232 31 $5,000,000 Josh Donaldson Braves 33 185 cm 155 .259 37 $23,000,000 Joey Votto Reds 36 188 cm 142 .261 15 $25,000,000 Cody Bellinger Dodgers 24 193 cm 156 .305 47 $605,000 Ryan Braun Brewers 35 188 cm 144 .285 22 $19,000,000 Maikel Franco Phillies 27 185 cm 123 .234 17 $5,200,000 Ian Kinsler Padres 37 183 cm 87 .217 9 $3,750,000 Marcell Ozuna Cardinals 28 185 cm 130 .241 29 $12,250,000 Calculate the Five Number Summary for the players' heights. Min: Q 1 : Median: Q 3 : Max:

Answer 1

We have to summary some statistics measures about the player's height.

We first start listing and sorting the data for the heights:

173 --> Min

183

183

183 --> Q1

185

185

185

185 --> Median (Q2)

185

185

188

188 --> Q3

188

188

193 --> Max

The number of data points is 15.

The minimum value is 173 cm.

Then, the Q1 will correspond to the value for which 25% of the data is below this value.

For 15 data points, 25% will correspond to 3.75. Then, we can consider the Q1 to be the fourth point from least to greatest.

Then, its value is Q1 = 183.

The median divides the data set in two halves. Then, as we have 15 data points, the 8th data point will correspond to the median.

Then, the median is Q2 = 185.

The Q3 is the data point for which 75% of the data is below that value. In this cas correspond to the 12th value: Q3 = 188.

Lastly, the maximum value is the last of the sorted list: Max = 193.

Answer:

Minimum = 173 cm

Q1 = 183 cm

Median = 185 cm

Q3 = 188 cm

Maximum = 193 cm