Question

number of students in each class at southeastern middle school
michela says that the modes of the two data are the same so the median and mean must also be the same. what is michela’s error?
the modes are not the same.
the means and medians are not the same.
only the modes and the medians are the same.
only the modes and the means are the same.

Explanation:

First, identify the mode from the dot plot: the mode is 23, as it has the most data points. Next, calculate the median: there are 20 data points, so the median is the average of the 10th and 11th values, which are both 24, so median = 24. Calculate the mean: sum all values ($20 + 21*2 + 22*2 + 23*4 + 24*3 + 25*2 + 26*2 + 27*2 + 28 + 29 = 480$), then divide by 20: $\frac{480}{20}=24$. Michela's error is assuming same modes force same medians/means, but here modes are same, but medians/means differ from the mode, and her core mistake is the false claim that same modes guarantee same medians/means, which is disproven because the means and medians are not the same as each other or the mode in this case, and her logic is invalid because equal modes do not require equal medians or means.

Answer:

The means and medians are not the same.