In the data set below, what are the lower quartile, the median, and the upper quartile? 54, 55, 63, 67, 75, 76 lower quartile = _____ median = _____ upper quartile = _____

Find Median: Arrange the data set in ascending order and find the median. The data set is already in ascending order: 54, 55, 63, 67, 75, 76. Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers. Median = (63 + 67) / 2 = 130 / 2 = 65.Identify Lower Quartile: Identify the data set for the lower quartile. For the lower quartile, consider the first half of the data set, excluding the median if necessary. First half is 54, 55, 63. Lower quartile data: 54, 55, 63.Calculate Lower Quartile: Find the value of the lower quartile. Lower quartile data: 54, 55, 63. For an odd number of observations, the lower quartile is the median of this subset. Lower quartile is 55.Identify Upper Quartile: Identify the data set for the upper quartile. For the upper quartile, consider the second half of the data set, excluding the median if necessary. Second half is 67, 75, 76. Upper quartile data: 67, 75, 76.Calculate Upper Quartile: Find the value of the upper quartile. Upper quartile data: 67, 75, 76. For an odd number of observations, the upper quartile is the median of this subset. Upper quartile is 75.Write Quartile Values: Write the values of the lower quartile, median, and the upper quartile. Lower quartile = 55 Median = 65 Upper quartile = 75

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $54, 55, 63, 67, 75, 76$ $\newline$ lower quartile $=$ $\_\_$ $\newline$ median $=$ $\_\_$ $\newline$ upper quartile $=$ $\_\_$

View step-by-step help

Home

Math Problems

Algebra 1

Calculate quartiles and interquartile range

Full solution

Q. In the data set below, what are the lower quartile, the median, and the upper quartile?

\newline

54, 55, 63, 67, 75, 76

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Find Median: Arrange the data set in ascending order and find the median. $\newline$ The data set is already in ascending order: $54, 55, 63, 67, 75, 76$ . $\newline$ Since there are $6$ numbers, the median will be the average of the $3$ rd and $4$ th numbers. $\newline$ Median $= (63 + 67) / 2 = 130 / 2 = 65$ .
Identify Lower Quartile: Identify the data set for the lower quartile. $\newline$ For the lower quartile, consider the first half of the data set, excluding the median if necessary. $\newline$ First half is $54$ , $55$ , $63$ . $\newline$ Lower quartile data: $54$ , $55$ , $63$ .
Calculate Lower Quartile: Find the value of the lower quartile. $\newline$ Lower quartile data: $54, 55, 63$ . $\newline$ For an odd number of observations, the lower quartile is the median of this subset. $\newline$ Lower quartile is $55$ .
Identify Upper Quartile: Identify the data set for the upper quartile. $\newline$ For the upper quartile, consider the second half of the data set, excluding the median if necessary. $\newline$ Second half is $67$ , $75$ , $76$ . $\newline$ Upper quartile data: $67$ , $75$ , $76$ .
Calculate Upper Quartile: Find the value of the upper quartile. $\newline$ Upper quartile data: $67$ , $75$ , $76$ . $\newline$ For an odd number of observations, the upper quartile is the median of this subset. $\newline$ Upper quartile is $75$ .
Write Quartile Values: Write the values of the lower quartile, median, and the upper quartile. $\newline$ Lower quartile = $55$ $\newline$ Median = $65$ $\newline$ Upper quartile = $75$