Question

Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range

Answer 1

58, 66, 79, 84, 87 (see explanation for the exact answer)

Explanation:

{58, 66, 79, 84, 87}

minimum = 58

lower quartile = 66

median = 79

upper quartile = 84

maximum = 87

Answer 2

Answer + Step-by-step explanation:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

The data set is in order then :

the minimum = 58

The maximum = 87

Determining the median :

first ,we notice that the data set has an even number (14) of numbers

Then

The median is the average of the two central values of the data set :

the two central values are the 7th and 8th numbers:

`\text{median} =(79+79)/(2) =79`

Determining the lower quartile :

The lower quartile is the median of the set :

58, 60, 65, 67 , 68, 72, 79

this set has an odd number (7) of values

Then

The central value is 67

Therefore

The lower quartile is 67

Determining the upper quartile :

The upper quartile is the median of the set :

79, 80, 81, 82 , 86, 86, 87

this set has an odd number (7) of values

Then

The central value is the 4th number which is 82

Therefore

The upper quartile is 82

Interquartile range :

82 - 67 = 15