Video: Determining the Mean, Median, and Mode for a Given Data Set

The scores earned on a math test are 86, 80, 76, 68, 73, 85, 74, 70, 71, and 70. Find the mean, median, and mode for the set of data.

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Video Transcript

The scores earned on a math test are 86, 80, 76, 68, 73, 85, 74, 70, 71, and 70. Find the mean, median, and mode for the set of data.

We recall that in order to calculate the mean from a data set, we firstly need to add all the values. In this question, this is the sum of the scores in the test. We then need to divide this total by the number of values, in this case, 10. The sum of the scores is 753. 753 divided by 10 is 75.3. This means that the mean of the scores is 75.3 marks.

We can calculate the median by finding the middle value. Before doing this, we must order the numbers from smallest to largest or largest to smallest. In ascending order, the scores are 68, 70, 70, 71, 73, 74, 76, 80, 85, and 86. As they are an even number of values, in this case, 10, there will be two middle numbers. These are 73 and 74. The median will be the value halfway between these two numbers, or the mean of the two numbers. This is equal to 73.5. Therefore, the median score is 73.5.

The mode is the most frequently occurring value or values in our data set. In this question, eight of the values appear once, and 70 appears twice. As 70 occurs more often than any other data value, the mode of the scores is 70. This set of data has a mean of 75.3, a median of 73.5, and a mode of 70.

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