MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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.