Figuring out the mean, median, mode and midrange

Question

Listed below are the playing times (in seconds) of songs that were popular at the time of this writing. Find the (a) mean, (b)median, (c) mode, and (d) midrange for the given sample data. Is there one time that is very different from the other? 444 245 234 246 246 290 278 228 239 218 266 236 218 258 260 259

Answer 1

putting the data in order from smallest to largest...

218,218,228,234,236,239,245,246,246,258,259,260,266,278,290,444

a) mean=4165/16=260.3125

b) median=246 (there is an even number of numbers so there are two middle numbers but they are both 246)

c) mode=218 and 246 because they both occur twice

d) midrange=(218+444)/2=662/2=331

444 is very different from all the others; all the data are in the 200's except 444 which is called an outlier

Answer 2

Hi Mark,

A 'mean' is the average of the numbers.  The first step is to find the sum of all the numbers.  The second step is to divide that sum by the number of pieces of data.  The sum is 4165 and there are 16 songs, so 4165 divided by 16 is 260.3125.  Follow the directions for the problem to see if you need to round off the answer, i.e. to the nearest 1 second. 

The 'median' is the middle number.  Notice the words 'median' and 'middle' each have 6 letters.  You need to list them in order from smallest to largest, so from 218 up to 444.  Since there is an even number of songs, there is no 'middle number'.  So, you find the average of the 2 middle numbers.  Since the two middle numbers are both 246, then median is simply 246.

The 'mode' is the number that appears most often.  Notice the word 'mode' and 'most' each have 4 letters.  Since 218 and 246 each appear twice, there are two modes: 218 and 246.

Is there a number very different from the others?  You bet.  The 444 is over 100 more seconds that the next longest song.

Have a good day!

Mary Ann

 

Answer 3

To calculate the mean of a set of data, add all the numbers up, and divide by the number of data points. This is your standard "average".

 

To find the median of a set of data, organize the data in numerical order. The median will be the number that is directly in the center. If there are an even number of data points, you'll take the mean of the central two numbers.

 

The mode of a data set is the data value that occurs most often. If more than one data point occurs the most frequently, then there is more than one mode. If all data points occur with the same frequency, there is no mode.

 

The midrange of a data set is the mean of the minimum and maximum values, (max + min)/2