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

(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 = ∑ =

                  X

                  X

                  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 = 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 = ∑ =

                  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

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

s

step-by-step explanation: