MATH SOLVE

2 months ago

Q:
# Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range. 20, 22, 25, 28, 29, 30, 32, 33, 34. Be sure to show your work for finding:The lower quartileThe upper quartileThe interquartile rangePLs help

Accepted Solution

A:

see the attached picture:

1st find the median, which would be the middle of the data set. Since there are 9 numbers the median would be the middle number of the set, this would give you the same amount of numbers on each side of it. The numbers to the left would be the lower and the numbers on the right would be the upper

so in the given data set the median is 29

the lower quartile is the median of the lower numbers, in this case the numbers below 29 are 20, 22 , 25, 28

since there is an even amount of numbers you need to add the 2 middle numbers together and divide by 2 to find the lower quartile so 22 +25 = 47, 47 / 2 = 23.5 this is the lower quartile

the upper quartile is found the same way, but using the upper numbers so in this case using 30, 32, 33 , 34

add the 2 middle numbers 32 +33 = 65 divide by 2 = 65/ 2 = 32.5 this is the upper quartile

the inter quartile range is subtracting the lower quartile from the upper quartile: 32.5 - 23.5 = 9

9 is the inter quartile range

1st find the median, which would be the middle of the data set. Since there are 9 numbers the median would be the middle number of the set, this would give you the same amount of numbers on each side of it. The numbers to the left would be the lower and the numbers on the right would be the upper

so in the given data set the median is 29

the lower quartile is the median of the lower numbers, in this case the numbers below 29 are 20, 22 , 25, 28

since there is an even amount of numbers you need to add the 2 middle numbers together and divide by 2 to find the lower quartile so 22 +25 = 47, 47 / 2 = 23.5 this is the lower quartile

the upper quartile is found the same way, but using the upper numbers so in this case using 30, 32, 33 , 34

add the 2 middle numbers 32 +33 = 65 divide by 2 = 65/ 2 = 32.5 this is the upper quartile

the inter quartile range is subtracting the lower quartile from the upper quartile: 32.5 - 23.5 = 9

9 is the inter quartile range