Question

Given the following data set, calculate the mean, median, mode, and midrange. 11,29,13,26,40,16,25,16,14,29

Please give answers or show work on how to figure out which is the mean and median and mode and midrange

Answer 1

Mean: 21.9

Median: 20.5

Mode: 16, 29

Midrange: 29

Explanation:

To find the mean of 11,29,13,26,40,16,25,16,14,29, add all the values together and divide by the number of values in the set. The result is your mean.

To find the median: the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

To find the mode: put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.

To find the midrange: add together the least and greatest values and divide by two, or in other words, find the mean of the least and greatest values.

Answer 2

Explanation:

The given set of data is

11,29,13,26,40,16,25,16,14,29

1) The formula for determining the mean is

Sum of items/total number of items.

Sum of items = 11 + 29 + 13 + 26 + 40 +16 + 25 + 16 + 14 + 29 = 219

Number of items = 10

Mean = 219/10 = 21.9

2) The median is the middle number. To determine the median, we would rearrange the numbers in an increasing or a decreasing order. It becomes

11, 13, 14, 16, 16, 25, 26, 29, 29, 40

Since the number of items is even, the median is the average of the two middle numbers. Therefore

Median = (16 + 25)/2 = 20.5

3) The mode is the number that occurs most frequently. 16 and 29 appeared twice. The rest appeared just once. So the mode is 16 and 29

4) The midrange is determined by finding the average of the sum of the item with the highest value and the item with the lowest value. The lowest number is 11, the highest number is 40.

Midrange = (40 + 11)/2 = 25.5