Question

FOR THE DATA: 63 76 88 75 82 82 94 61, FIND THE FOLLOWING:A) MEAN __________B) MEDIAN __________C) MODE __________D) MIDRANGE __________E) RANGE __________

Answer 1

GIVEN:

We are given the following data set;

`63,76,88,75,82,82,94,61`

Required;

To calculate the following;

`Mean,Median,Mode,Midrange\text{ }and\text{ }Range.`

Step-by-step solution;

To calculate the mean of a data set, we use the following formula;

`\begin{gathered} Mean=(\Sigma x)/(n) \\ \\ Where;\text{ }x=individual\text{ }data,\text{ }n=number\text{ }of\text{ }data \end{gathered}`

We now calculate as follows;

`\begin{gathered} Mean=(63+76+88+75+82+82+94+61)/(8) \\ \\ Mean=77.625 \end{gathered}`

To calculate the median we re-arrange the data set in order from least value to greatest value.

`61,63,75,76,82,82,88,94`

We now observe the number that lies in the middle of the set. We do this by counting the same number of individual data both from the left and from the right. The point where the number count meets is the midpoint and there we have our median value.

For this data set, the values in the middle of the set are;

`middle\text{ }values=76,82`

In a case where we have two numbers, we add them up and divide by 2. The result would now be the median of the data set.

Hence;

`\begin{gathered} Median=(76+82)/(2) \\ \\ Median=79 \end{gathered}`

The mode is the value that has the highest frequency. That is, the one which occurs most often in the entire data set. For the given data set, the mode is

`Mode=82`

The midrange is the value that lies midway between the least value and the highest value. In other words, we add up the least value and highest value and divide the result by 2. What we have after that is the midrange, that is;

`\begin{gathered} Midrange=(61+94)/(2) \\ \\ Midrange=77.5 \end{gathered}`

The range is the difference between the least value and the greatest value, that is;

`\begin{gathered} Range=94-61 \\ \\ Range=33 \end{gathered}`

Therefore, we now have our answers as follows,

ANSWER:

`\begin{gathered} Mean=77.625 \\ \\ Median=79 \\ \\ Mode=82 \\ \\ Midrange=77.5 \\ \\ Range=33 \end{gathered}`