Question

Calculate the mean, median, and mode of each of the following populations of numbers: (Round your mean and median value to 1 decimal place.) a. 9, 11, 10, 8, 15, 14, 9, 15, 8, 15 N (Population) MEAN MEDIAN MODE b. 131, 116, 90, 86, 117, 80, 90, 114, 137 N (Population) MEAN MEDIAN MODE

Answer 1

Answer:

(a) Mean = 10.4, Median = 10.5, Mode = 15

(b) Mean = 106.78, Median = 114, Mode = 90

Step-by-step explanation:

(a)

Given: 9, 11, 10, 8, 15, 14, 9, 15, 8, 15

(i) The Arithmetic Mean, X, is the sum of all the numbers in a data set divided by the quantity of numbers in that set.

         ⇒      X = $\frac{1}{n}$∑$_{i = 1}^{n}a_{i}$ = $\frac{a_{1} + a_{2} + a_{3} + ... + a_{n}}{n}$

                  X$= \frac{9 + 11 + 10 + 8 + 15+ 4 + 9 + 15 + 8 + 15}{10}$

                  X$= \frac{104}{10}$

                  X = 10.4

                  Mean = 10.4

(ii) Median

To get the median of an small data or ungrouped data;

1. Arrange the data in ascending or descending order.

2. Choose the middle value. If the middle value is a single value, then, that value is the median but if the middle values are two, the mean of the two middle values is evaluated to get the median.

Arranging the populations of numbers given in ascending order;

                     8, 8, 9, 9, 10, 11, 14, 15, 15, 15

The middle values are the two in bold. Since they are two values, the mean of the two is evaluated to get the median.

                            $median = \frac{10 + 11}{2}$

                            $median = \frac{21}{2}$

                            Median = 10.5

(iii) Mode is the data with the highest frequency. Considering the population of numbers given;

                             Number               Frequency

                                  8                             2

                                  9                             2

                                 10                             1

                                 11                              1

                                 14                             1

                                 15                             3

From the data analyzed above, number 15 has the highest frequency (3). Therefore, Mode = 15

(b) Using the approach above in (a) to solve (b);

Given: 131, 116, 90, 86, 117, 80, 90, 114, 137

(i)

Arithmetic Mean,  X = $\frac{1}{n}$∑$_{i = 1}^{n}a_{i}$ = $\frac{a_{1} + a_{2} + a_{3} + ... + a_{n}}{n}$

                  $X = \frac{131 + 116 + 90 + 86 + 117 + 80 + 90 + 114 + 137}{9}$

                  $X = \frac{961}{9}$

                  X = 106.78

                  Mean = 106.78

(ii) Arranging the populations of numbers given in ascending order;

                    80, 86, 90, 90, 114, 116, 117, 131, 137

The middle value is a single number 114 in bold. Therefore, the median is 114.

                   Median = 114

(iii) Considering the population of numbers given;

                             Number               Frequency

                                 80                             1

                                 86                             1

                                 90                             2

                                 114                             1

                                 116                             1

                                 117                             1

                                 131                             1

                                 137                            1

From the data analyzed above, number 90 has the highest frequency (2). Therefore, Mode = 90