On a test given to a class of 30 students. One student scored 50, one scored 60, one scored 80, one scored 90 and each of the rest scored 70.

Question

On a test given to a class of 30 students. One student scored 50, one scored 60, one scored 80, one scored 90 and each of the rest scored 70. Which of the following statements is true about the distribution of scores?  

A) The median is greater than the mode

B) The median is less than the mode

C) The mean is greater than the mode

D) The Mean and mode are equal  

Answer 1

Hello Cassandra,

The following are characteristics of your data set presented:

The median is 70.

The mean is 70.

The mode is 70.

Therefore, the correct answer to your question is D.

As a tutor, I feel an obligation to provide you some further information to assist you in the future in doing these problems in statistics.

First, the median, mode, and mean are all measures of central tendency. The range is also considered a measure of central tendency, however that was not part of your question. Second, the mean of a data set is the sum of all values in your data set divided by the number of scores in that set. In your case your data has 1 score of 50, another score of 60, twenty-six events of 70, one score of 80, and one score of 90.

When totaling the scores presented, we arrive at 2100. Dividing 30 cases or events into 2100 is how we arrived at the mean, okay?

The median is the middle value of scores. In fact, the median is often considered a better measure of central tendency due to outlier scores which can throw the arithmetic mean off. For example, imagine you have 30 scores of 70 and one score of 120. As you most likely are noticing, that score of 120 will pull the mean and will not be as accurate a reflection of the data.

To determine the median, I recommend you rank order your scores from lowest to highest. If you have an even number of scores, you need to take the two middle values and divide by two in order to obtain your median. If you have an odd number of scores, you will always use the middle score after you have rank ordered them.

The mode is the score that appears most frequently in a data set. Obviously, as I am sure you see, that value in your data set is 70.

Finally, I tell my students the following advice: Statistics may appear scary at first, but with a basic grasp of math, it is a walk in the park. This walk becomes even easier as you do the statistics because it will become second nature to you.

I hope I have assisted you and wish you a great week. Please feel free to leave any feedback, ask for further clarity, or ask any further questions related to the solution I provided you by clicking the "Add Comment" prompt. If you need one-on-one tutoring, feel free to reach out to me. Best!