Question

5. Dipak is trying to find the typical month the students in his class were born. He starts by numbering the months 1

through 12 and compiling his data set, as shown below.
1,4,5,6,7,7,8,9, 9, 10, 11, 11, 12, 12
He adds all the numbers up to get a total of 106, then divides by 14 to get 8. Dipak says the average month his
classmates were born in is August.
Does Dipak's strategy and answer make sense? Explain your reasoning

Answer 1

Dipak's strategy and answer do not make sense. While Dipak correctly calculated the average by adding up all the numbers and dividing by the total count, his interpretation of the average as the "typical month" is flawed.

In this scenario, the numbers represent the months in which the students were born. The average month of birth is not necessarily the same as the "typical" or most common month. To determine the most typical month, Dipak would need to analyze the frequency or count of each month and identify which month appears most frequently.

Let's examine the data set provided:

1, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12

By counting the occurrences of each month, we find that:

Month 1 appears once.
Month 4 appears once.
Month 5 appears once.
Month 6 appears once.
Month 7 appears twice.
Month 8 appears once.
Month 9 appears twice.
Month 10 appears once.
Month 11 appears twice.
Month 12 appears twice.

Based on this analysis, the most frequent or "typical" month in Dipak's class is actually the month of December (12), which appears twice. Therefore, Dipak's answer of August (8) is incorrect based on the given data.

Answer 2

No

Explanation:

No, Dipak's strategy and answer does not make sense. His strategy is an example of mean or average, which is useful for finding the central tendency in a data set. However, it does not give a good representation of the data set in this scenario because there are two months with more than one entry. It does not accurately reflect the data set and does not give a good indication of the typical month the students were born. A better approach would be to use the mode, which is the most frequently occurring value. In this case, the mode would be 7, indicating that July was the typical month that the students in Dipak's class were born.