MATH 1029 - 12.2

What is the median and how is it​ obtained?

The median of a data set is the data item in the middle of the ordered set. To find the​ median, first arrange the data items in​ order, from smallest to largest. If the number of data items is​ odd, the median is the data item in the middle of the list. If the number of data items is​ even, the median is the mean of the two middle data items.

What is the midrange and how is it​ obtained?

The midrange is a value that is representative of a data set. It is found by adding the lowest and highest data values and dividing the sum by 2.

In a class of 40​ students, 21 have examination scores of​ 77%. Which measure or measures of central tendency can you immediately​ determine? Explain your answer.

The mode is​ 77% because the majority of scores are​ 77%. The median is​ 77% because​ 77% will be the 20th and 21st data items in an ordered​ list, regardless of the other data items. No other measures can be determined.

When finding the​ mean, it is necessary to arrange the data items in order.

The statement is false. To make the statement​ true, change​ "mean" to​ "median".

Numbers representing what is average or typical about a data set are called measures of central tendency.

The statement is true because these numbers are generally located toward the center of a distribution.

​I'm working with a data set for which neither the mean nor the median is one of the data items.

The statement makes sense because it is possible to have a set of data that does not include the mean or median

Although the data set 3​, 3​, 4​, 5​, 5​, 5​, 6​, 6 has a number of repeated​ items, there is only one mode.

The statement makes sense because there is 1 mode in the data set

​the sum of all the data items divided by the number of data​items, is the measure of central tendency called the

mean

The measure of central tendency that is the data item in the middle of​ ranked, or​ ordered, data is called the

median

The measure of central tendency that is found by adding the lowest and highest data values and dividing the sum by 2 is called the

midrange

A data value that occurs most often in a data set is the measure of central tendency called the

mode

A company has twenty employees. Eighteen of them earn between​ $35,000 and​ $45,000 a year. Which is the best measure of​ salaries?

​Median, as the salary of the owner and his assistant are very high.