The image shows a problem related to a set of commuting distances for workers, along with their frequencies. Here’s a summary of the information presented:

1. Commuting Distance intervals are listed as:

   • $0-9$, $10-19$, $20-29$, $30-39$, $40-49$, $50-59$, $60-69$, $70-79$, $80-89$, $90-99$.

2. Frequencies corresponding to these intervals are:

   • $12, 22, 48, 26, 8, 3, 3, 1, 1, 1$.

The question is asking for the mean and standard deviation of the commuting distances.

To calculate these:

Mean Calculation

1. Find the midpoint of each distance interval.
2. Multiply each midpoint by its frequency.
3. Divide the sum of these products by the total number of workers (sum of all frequencies).

Standard Deviation Calculation

1. Use the midpoint values and calculate each deviation from the mean.
2. Square each deviation, multiply by the corresponding frequency, and sum them.
3. Divide by the total frequency to get the variance, and then take the square root for the standard deviation.

Would you like me to calculate the mean and standard deviation step-by-step with this data?

Questions to Explore

1. Would you like an explanation on calculating midpoints for intervals?
2. Do you need help understanding the concept of frequency distribution?
3. Should we discuss the differences between sample and population standard deviation?
4. Would you like to know how these statistics can be applied in real-world scenarios?
5. Are you interested in learning how these statistics can help in decision-making?

Tip:

Using midpoint approximations in grouped data allows for efficient calculation of mean and standard deviation.