[Verified] A Coach Compared The Heights Of The Players On Two Different Teams. The Data Set Is Shown In The Table Below

A Coach Compared The Heights Of The Players On Two Different Teams. The Data Set Is Shown In The Table Below

Heights Of The Players On Two Teams

Team A Player Heights (Inches)7668736560636976
Team B Player Heights (Inches)6373647070677562

Based on these data, which statement is true?

1. The mean height of the players on Team B is greater than the mean height of players on Team A.
2. The mean height of the players on Team A is greater than the mean height of players on Team B.
3. The median height of the players on Team B is greater than the median height of players on Team A.
4. The median height of the players on Team A is greater than the median height of players on Team B.

Explanation

Let’s break this down step by step.

1. Calculate the Mean Height for Each Team

Concept Used: The mean (or average) is calculated by summing up all the values in a set and then dividing by the number of values in that set.

Team A Mean Height Calculation:

Given heights: 76, 68, 73, 65, 60, 63, 69, 76

Step 1: Sum up all the heights Sum = 76 + 68 + 73 + 65 + 60 + 63 + 69 + 76

Step 2: Divide by the number of players (8 in this case) Mean Height of Team A=Sum8Mean Height of Team A=8Sum​

Team B Mean Height Calculation:

Given heights: 63, 73, 64, 70, 70, 67, 75, 62

Step 1: Sum up all the heights Sum=63+73+64+70+70+67+75+62Sum=63+73+64+70+70+67+75+62

Step 2: Divide by the number of players (8 in this case) Mean Height of Team B=Sum8Mean Height of Team B=8Sum​

Let’s calculate these values.

Team A Median Height Calculation Results:

Given heights in ascending order: 60, 63, 65, 68, 69, 73, 76, 76

Median Height of Team A = 68+692=68.5268+69​=68.5 inches

Team B Median Height Calculation Results:

Given heights in ascending order: 62, 63, 64, 67, 70, 70, 73, 75

Median Height of Team B = 67 + 702=68.5267+70​=68.5 inches

From the above calculations, we can see that the median height of both Team A and Team B is 68.5 inches. Therefore, the median heights of both teams are equal.

Conclusion on A Coach Compared The Heights Of The Players On Two Different Teams

  1. The mean height of the players on Team A (68.75 inches) is greater than the mean height of players on Team B (68 inches). So, statement 2 is true.
  2. The median height of the players on both teams is the same (68.5 inches). Therefore, neither statement 3 nor statement 4 is true.

Final Answer

The true statement is: 2. The mean height of the players on Team A is greater than the mean height of players on Team B

Leave a Reply