Question

Jessica’s Spanish test scores are 98, 74, 88, 83, 91, and 85. Find the range, median, first and third quartiles, and interquartile range of her scores. Use the measures of variation to describe the data.

Answer 1

Answer:

Range = 24; Median = 87.5; Q1 = 83; Q3 = 91; IQR = 8

Step-by-step explanation:

98, 74, 88, 83, 91, 85

(a) Sort the numbers

74, 83, 85, 88, 91, 98

(b) Range

Max. = 98; min. = 74

Range = max. - min. = 98 - 74 = 24

(c) Median

The median (Q2) is the middle number when we arrange the observations in order.

There is an even number of observations, so the median is the average of the third and fourth values.

The average of 85 and 88 is 87.5, so the median is 87.5.

Half of Jessica's grades are above 87.5 and half are below.

(d) First quartile

(74, 83, 85), (88, 91, 98)

The first quartile (Q1) is the median of the numbers below Q2.

The median of 74, 83, and 85 is 83.

First quartile = 83

One fourth of Jessica's grades would be below  83.

(e) Third quartile

The median of 88, 91, and 98 is 91.

Third quartile = 91

One fourth of Jessica's grades would be above 91.

(f) IQR

IQR = Q3 - Q1 = 91 - 83 = 8.

Half of Jessica's grades would be in the range 83 to 91.

Answer 2

Answer:

Range = 24, Median = 86.5, Q1 =  83, Q3 = 91, IQR = 8

Step-by-step explanation:

Jessica's Spanish test scores are :

98, 74, 88, 83, 91, and 85

First we arrange these value in lowest to greatest.

74, 83, 85, 88, 91, 98

Range = Greatest - Lowest

           = 98 - 74

          = 24

Median is the middle number of the data set, but there are two numbers in the middle, so take mean of the middle numbers to get median.

Median =$\frac{(85+88)}{2}$

            =  86.5

First Quartile (Q1) is the median of lower half of the data set

74, 83, 85

Third Quartile (Q3) is the median of the upper half of the data set.   88, 91, 98

Q1 = 83

Q3 = 91

Inter Quartile Range (IQR) = To get IQR subtract Q1 from Q3.

Q3 - Q1

                                             = 91 - 83

                                          = 8