Question

21. 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).NameTeamAgeHeightGAVEHRSalaryCedric MullinsOrioles25173 cm22.0940$557,500Tim AndersonWhite Sox26185 cm123.33518$1,400,000Christin StewartTigers25183 cm104.23310$556,400Alex GordonRoyals35185 cm150.26613$20,000,000Jonathan SchoopTwins27185 cm121.25623$7,500,000Marcus SemienAthletics29183 cm162.28533$5,900,000Yandy DiazRays28188 cm79.26714$558,400Randal GrichukBlue Jays28188 cm151.23231$5,000,000Josh DonaldsonBraves33185 cm155.25937$23,000,000Joey VottoReds36188 cm142.26115$25,000,000Cody BellingerDodgers24193 cm156.30547$605,000Ryan BraunBrewers35188 cm144.28522$19,000,000Maikel FrancoPhillies27185 cm123.23417$5,200,000Ian KinslerPadres37183 cm87.2179$3,750,000Marcell OzunaCardinals28185 cm130.24129$12,250,000Calculate the Five Number Summary for the number of games played by the players.Min: Q1 : Median: Q3 : Max:

Answer 1

Given:

The number of games played by 15 players are,

22, 123, 104, 150, 121, 162, 79, 151, 155, 142, 156, 144, 123, 87, 130.

The objective is to find five number summary for the number of games.

Step-by-step explanation:

The five number summary are minimum value, quartile 1, median, quartile 2 and maximum value.

Increasing order:

The increasing order of the given data is,

22, 79, 87, 104, 121, 123, 123, 130, 142, 144, 150, 151, 155, 156, 162.

Minimum and Maximum value:

By considering the increasing order of the data, the minimum value is 22 and the maximum value is 162.

To find median:

The median can be calculated as the middle term of total number of data.

Since, the total number of data is 15, which is odd, then the median can be calculated as,

`\begin{gathered} \text{Median}=(15+1)/(2) \\ =(16)/(2) \\ =8th\text{ term} \end{gathered}`

Thus, the 8th term of increased order is 130.

To find Q1:

The quartile 1 can be defined as the middle term of the left side of the median.

Since, the left side of the median contains 7 terms, which is odd, then the quartile 1 can be calculated as,

`\begin{gathered} Q1=(7+1)/(2) \\ =(8)/(2) \\ =4th\text{ term (left)} \end{gathered}`

Thus, the 4th term on left side of median is 104.

To find Q3:

The quartile 3 can be defined as the middle term of the right side of the median.

Since, the right side of the median contains 7 terms, which is odd, then the quartile 3 can be calculated as,

`\begin{gathered} Q3=(7+1)/(2) \\ =(8)/(2) \\ =4th\text{ term (right)} \end{gathered}`

Thus, the 4th term on right side of median is 151.

Hence, the five number summary are,

Min: 22

Q1: 104

Median: 130

Q3: 151

Max: 162.