Questions: A sample of college students was asked how much they spent monthly on cell phone plans. Approximate the mean for the cost. Monthly cell phone plan cost () Number of students 10.00-19.99 6 20.00-29.99 26 The mean for the cost is .

Solution Steps

We have the following data regarding the monthly cell phone plan costs and the number of students in each cost range:

\[ \begin{array}{|c|c|} \hline \text{Monthly cell phone plan cost (\$)} & \text{Number of students} \\ \hline 10.00-19.99 & 6 \\ 20.00-29.99 & 26 \\ 30.00-39.99 & 14 \\ 40.00-49.99 & 10 \\ \hline \end{array} \]

To find the mean, we first calculate the midpoints of each cost range:

\[ \begin{align_} \text{Midpoint of } 10.00-19.99 & = \frac{10.00 + 19.99}{2} = 14.995 \\ \text{Midpoint of } 20.00-29.99 & = \frac{20.00 + 29.99}{2} = 24.995 \\ \text{Midpoint of } 30.00-39.99 & = \frac{30.00 + 39.99}{2} = 34.995 \\ \text{Midpoint of } 40.00-49.99 & = \frac{40.00 + 49.99}{2} = 44.995 \\ \end{align_} \]

Next, we calculate the weighted sum of the midpoints based on the number of students:

\[ \text{Weighted Sum} = (14.995 \times 6) + (24.995 \times 26) + (34.995 \times 14) + (44.995 \times 10) \]

Calculating each term:

\[ \begin{align_} 14.995 \times 6 & = 89.97 \\ 24.995 \times 26 & = 649.87 \\ 34.995 \times 14 & = 489.93 \\ 44.995 \times 10 & = 449.95 \\ \end{align_} \]

Thus, the total weighted sum is:

\[ \text{Weighted Sum} = 89.97 + 649.87 + 489.93 + 449.95 = 1679.72 \]

The total number of students is:

\[ N = 6 + 26 + 14 + 10 = 56 \]

Now, we can calculate the mean cost:

\[ \mu = \frac{\text{Weighted Sum}}{N} = \frac{1679.72}{56} \approx 29.99 \]

Final Answer