Question

think about the process the following dot plots show the ages of two groups of tourists. what is the first step age for each group? make a comparative inference based on the mean values.

what is the first step to finding the mean age for each group?
a. the first step should be to count the number of dots for each age.
b. the first step should be to find the middle number of all the dots.
c. the first step should be to count the ages that have dots and just average those numbers.
d. the first step should be to average the minimum and maximum values that have dots.

the mean age for group 1 is \\(\square\\) years.

Explanation:

Step1: Confirm first step for mean

The first step to calculate the mean from a dot plot is to count the number of dots (frequency) for each age, which corresponds to option A.

Step2: List Group 1 ages & frequencies

From Group 1's dot plot:

• Age 41: 1 dot, Age 42: 1 dot, Age 43: 2 dots, Age 44: 2 dots, Age 45: 2 dots, Age 46: 1 dot, Age 47: 1 dot

Step3: Calculate total age sum

$$(41\times1)+(42\times1)+(43\times2)+(44\times2)+(45\times2)+(46\times1)+(47\times1)$$
$$=41+42+86+88+90+46+47=440$$

Step4: Calculate total number of tourists

$$1+1+2+2+2+1+1=10$$

Step5: Compute mean age

$$\text{Mean} = \frac{\text{Total Age Sum}}{\text{Total Tourists}} = \frac{440}{10}=44$$

Answer:

A. The first step should be to count the number of dots for each age.
The mean age for Group 1 is 44 years.