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# What is the mean mode and median of this data 64 80 64 70 76 79 67 72 65 73 68 65 67 65 70 62 67 68 65 64?

step 1. arrange the numbers in ascending order (from low to high) as follows.

was: 64 80 64 70 76 79 67 72 65 73 68 65 67 65 70 62 67 68 65 64

now: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80

step 2. count the number of the numbers above, or assign an index as follows.

string: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80

index: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

so the count is 20.

The mode is the number most frequently observed. The mode is 65, which occurs four times.

The median is the number in the middle. In this case, the 10th and 11th numbers both qualify for consideration. We take the average of the two numbers. The median is therefore 67.

Alternate methods:

1) Use Microsoft Excel statistical functions of =mode() and =median()

2) Draw a bar graph with the horizontal axis of integers from 62 to 80. The y-axis is the frequency observed for that specific x value. For example, the frequency for 62 is one. The frequency for 63 is zero, and so on. The mode is the bar with the highest count. The median is not so obvious from a bar graph, unless the distribution is symmetric. Need some manual counting.