Question

I.Calculate and explain how to find the mean, the median of the following numbers:189,000, 100,000, 83,000, 135,000, 148,000, 205,000, 180,000, 150,000, 200,000 and 210,000

Answer 1

A.) The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Given the following data, let's calculate the mean:

`\text{ Mean = }\frac{\text{ Sum of all numbers}}{\text{ No. of data}}`

Sum of all numbers = 189,000 + 100,000 + 83,000 + 135,000 + 148,000 + 205,000 + 180,000 + 150,000 + 200,000 + 210,000

Sum of all numbers = 1,600,000

No. of data = 10

We get,

`\text{ Mean = }\frac{\text{ 1,600,000}}{\text{ 10}}\text{ = 160,000}`

Therefore, the mean is 160,000

B.) The median is the middle value when a data set is ordered from least to greatest.

Given the data:

189,000, 100,000, 83,000, 135,000, 148,000, 205,000, 180,000, 150,000, 200,000, 210,000

Let's first arrange it from least to greatest.

83,000, 100,000, 135,000, 148,000, 150,000, 180,000, 189,000, 200,000, 205,000, 210,000

The number of data is an even number. Therefore, to get the median, we will be getting the average of the two middle numbers.

The two middle numbers are 150,000 and 180,000

Let's calculate the median:

`\text{ Median = }\frac{150,000\text{ + 180,000}}{2}\text{ = }\frac{\text{ 330,000}}{2}`
`\text{ Median = 165,000}`

Therefore, the median is 165,000