Question

the frequency table shows the length of time, in years, that the members of a soccer team have been playing soccer.

number of years played	number of players
4	2
5	6
6	3
7	5

the teams coach has been playing soccer for 26 years. how does including the number of years the coach has played affect the following measures?

increases	decreases	remains the same

|mean|
|median|
|mode|
|range|

Explanation:

Step1: Recall the definitions

Mean is the sum of all values divided by the number of values. Median is the middle - value when data is ordered. Mode is the most frequently occurring value. Range is the difference between the maximum and minimum values.

Step2: Analyze the mean

The sum of the players' years - playing values is relatively small compared to the large value of 26. Adding 26 will increase the sum and the number of data points. Since the sum increases more proportionally than the number of data points, the mean will increase.

Step3: Analyze the median

There are \(2 + 2+6 + 3+5=18\) players originally. The median is the average of the 9th and 10th ordered values. When we add the coach's 26 years, there are 19 data points. The median will be the 10th value. Since 26 is a large out - lier, the median will increase slightly or remain the same depending on the original order, but in most cases with such a large outlier, it will increase.

Step4: Analyze the mode

The mode is the number of years played that occurs most frequently. Currently, the mode is 5 (since 6 players have played for 5 years). Adding the coach's 26 years does not change the most frequently occurring value among the players, so the mode remains the same.

Step5: Analyze the range

The original range is \(7 - 3=4\). The new maximum value is 26 and the minimum is still 3. So the new range is \(26 - 3 = 23\), which means the range increases.

Answer:

Mean: Increases
Median: Increases
Mode: Remains the same
Range: Increases