Question

the ages of the members of four teams are summarized below. answer the questions about them.
team a: the mean age is 37 and the range of ages is 22.
team b: the mean age is 35 and the range of ages is 21.
team c: the mean age is 36 and the range of ages is 26.
team d: the mean age is 43 and the range of ages is 19.
(a) based on the information above, which teams ages have the most variability?
○ team a
○ team b
○ team c
○ team d
(b) based on the information above, which team has the youngest members on average?
○ team a
○ team b
○ team c
○ team d

Explanation:

Step1: Calculate the range for each team

The range is calculated as \(Range = Maximum - Minimum\).
For Team A: \(Range_A=37 - 22 = 15\).
For Team B: \(Range_B=35 - 21 = 14\).
For Team C: \(Range_C=36 - 26 = 10\).
For Team D: \(Range_D=43 - 19 = 24\).

Step2: Compare the ranges

Since \(24>15>14>10\), Team D has the largest range, which means Team D has the most variability.

We are not given the data to calculate the average directly. But if we assume that the range is related to the spread of data. A larger range may not directly imply a lower average. However, if we consider the formula for the range \(R = max - min\). For Team D, \(max = 43\) and \(min=19\). For Team A, \(max = 37\), \(min = 22\); Team B: \(max=35\), \(min = 21\); Team C: \(max = 36\), \(min=26\).
If we assume a simple case of two - data - point set (for the sake of illustration, though the actual number of data points is not given). The average of two numbers \(x\) and \(y\) is \(\bar{x}=\frac{x + y}{2}\).
For Team D: If we assume two values \(19\) and \(43\), \(\bar{x}_D=\frac{19 + 43}{2}=\frac{62}{2}=31\).
For Team A: If we assume two values \(22\) and \(37\), \(\bar{x}_A=\frac{22+37}{2}=\frac{59}{2}=29.5\).
For Team B: If we assume two values \(21\) and \(35\), \(\bar{x}_B=\frac{21 + 35}{2}=\frac{56}{2}=28\).
For Team C: If we assume two values \(26\) and \(36\), \(\bar{x}_C=\frac{26+36}{2}=\frac{62}{2}=31\). But if we consider more data points (since range is \(max - min\) and mean is \(\frac{\sum_{i = 1}^{n}x_i}{n}\)). A smaller range (Team B has range \(14\)) may have a more "compressed" data set towards the lower end.

Answer:

(a) Team D