Answer to Question #327148 in Statistics and Probability for beb

Question

Compute for the mean, the median, and the mode of each set of ungrouped data. Write your answer on the table below.

1.) 12, 31, 29, 6, 10, 8, 13, 27, 24, 16

2.) 52, 52, 52, 50, 55, 50, 57, 49, 60, 49, 62

3.) 35, 42, 36, 40, 49, 33, 39, 37, 44, 28, 43

4.) 62, 49, 60, 49, 57, 50, 55, 50, 52, 52, 52

5.) 11, 30, 28, 5, 9, 7, 12, 26, 23, 15

Answer 1

Mean is equal to the sum of all elements, divided by their amount

We should sort each row to find the medians.

Median is calculated from sorted sample with this rules:

1) If sample size is odd then median is equal to the element located in the center of the sample

(in other words, if sample size is 2n + 1, then median is the element at (n + 1)'th position

2) Else (sample size is even) median is half of the sum of two elements located in the center of the sample (in other words, if sample size is 2n, then median is equal to the half of the sum of elements at n'th and (n + 1)'th positions

Mode is the element that appears in sample with the highest frequency

If there are more then one values with the same highest frequency, mode doesn't exist;

in this case we will denote mode as 'none'

Let's sort each sample and find these values:

1) Sorted: 6, 8, 10, 12, 13, 16, 24, 27, 29, 31

Mean = (6 + 8 + 10 + 12 + 13 + 16 + 24 + 27 + 29 + 31) / 10 = 17.6

Median = (13 + 16) / 2 = 14.5

Mode = none

2) Sorted: 49, 49, 50, 50, 52, 52, 52, 55, 57, 60, 62

Mean = (49 + 49 + 50 + 50 + 52 + 52 + 52 + 55 + 57 + 60 + 62) / 11 = 53.4545

Median = 52

Mode = 52

3) Sorted: 28, 33, 35, 36, 37, 39, 40, 42, 43, 44, 49

Mean = (28 + 33 + 35 + 36 + 37 + 39 + 40 + 42 + 43 + 44 + 49) / 11 = 38.7273

Median = 39

Mode = none

4) Sorted: 49, 49, 50, 50, 52, 52, 52, 55, 57, 60, 62

Mean = (49 + 49 + 50 + 50 + 52 + 52 + 52 + 55 + 57 + 60 + 62) / 11 = 53.4545

Median = 52

Mode = 52

5) Sorted: 5, 7, 9, 11, 12, 15, 23, 26, 28, 30

Mean = (5 + 7 + 9 + 11 + 12 + 15 + 23 + 26 + 28 + 30) / 10 = 16.6

Median = (12 + 15) / 2 = 13.5

Mode = none

$~~~~~~~~~Mean~~~~~Median~~~~~Mode\\ ~~~~1~~~~~17.6~~~~~~~~~~14.5~~~~~~~~~none\\ ~~~~2~~~~~53.45~~~~~~~~~~52~~~~~~~~~~~~52\\ ~~~~3~~~~~38.73~~~~~~~~~~39~~~~~~~~~~~none\\ ~~~~4~~~~~53.45~~~~~~~~~~52~~~~~~~~~~~~~52\\ ~~~~5~~~~~~16.6~~~~~~~~~~13.5~~~~~~~~~none$