Question

the weights (to the nearest five pounds) of 36 randomly selected male college students are organized in the histogram. use the graph to find the mean weight. the mean weight is pounds (round to the nearest thousandth as needed.)

Explanation:

Step1: Determine mid - points of weight intervals

Assume the weight intervals are: 110 - 115, 115 - 120, etc. The mid - points $x_i$ for each interval are calculated as $\frac{\text{lower limit}+\text{upper limit}}{2}$. For example, for 110 - 115, $x_1=\frac{110 + 115}{2}=112.5$. Calculate mid - points for all intervals.

Step2: Determine frequencies $f_i$

Read the frequencies from the histogram for each weight interval. Let the frequencies be $f_1,f_2,\cdots,f_n$.

Step3: Calculate the sum of the products $f_ix_i$

For each interval, calculate $f_ix_i$ and sum them up: $\sum_{i = 1}^{n}f_ix_i$.

Step4: Calculate the total frequency

Sum up all the frequencies: $N=\sum_{i=1}^{n}f_i = 36$.

Step5: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{N}$.

Since the histogram data is not fully presented with actual values of mid - points and frequencies, we cannot perform the full calculation. But the general formula for the mean of grouped data from a histogram is $\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{\sum_{i=1}^{n}f_i}$.

Answer:

Without specific values from the histogram for mid - points and frequencies, we cannot provide a numerical answer. If we had the values, we would follow the above steps to calculate the mean weight.