Question

40 points fast For the following set of test scores, identify:

• The mean
• The median
• The mode
• The range
• The interquartile range

50, 55, 70, 75, 82, 82, 90
Which measure of center would this student want his teacher to use--the mean or the median? plz fast 40 points

Answer 1

The measure of center would this student want his teacher to use is the

median
`= {\bf 75}`

Mean
`= {\bf 5}` , Mode
`={\bf 82}` , Range
`={\bf40}` and Interquartile Range
`= {\bf 32}`

Explanation:

Given Data set
`= 50,55,70,75,82,82,90`

Number of elements in data set
`= 7`

To find Mean

The ‘Mean” is the average of a set of numbers.

The "Mean" is computed by adding all of the numbers in the data together and dividing by the number of elements contained in the data set.

Mean
`= \frac{50 +55 +70 + 75 + 82 + 82 + 90} {7 }`

Mean
`= (504)/(7)`

Mean
`= 5`

Median

The “Median” is the middle value of a set of ordered numbers.

Therefore Median
`=75`

Mode

The "Mode" for a set of data is the value that occurs most often.

It is not uncommon for a data set to have more than one mode. This happens when two or more elements occur with equal frequency in the data set.

Therefore Mode
`=82`

Range

The "Range" is the difference between the largest value and smallest value in a set of data.

Range
`= 90-50`

Range
`= 40`

Interquartile Range

The “Interquartile Range” is the difference between smallest value and the largest value of the middle 50% of a set of data.

The "Interquartile Range" is from Q1 to Q3:

To find the interquartile range of a set of data:

The cut the list into four equal parts

. The quartiles are the “cuts”

The interquartile range is the distance between the two middle sets of data

Interquartile Range
`= Q_3-Q_1`

Interquartile Range
`= 82-50`

Interquartile Range
`= 32`