LOWER AND UPPER QUARTILES SHEET 2 - Find Quartiles and Interquartile Range

Oct 22, 2026

Uploaded by Mary Man

Worksheets and answer key for computing lower quartile, median, upper quartile, and interquartile range from four given sets of numerical data. The problems instruct sorting each dataset into order, then applying quartile rules for both odd and even term counts. A structured results table records the ordered list, quartile values, and the interquartile range calculation for each data set, including one with decimal values.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

Find lower and upper quartiles

Set 1 to Set 4

Answers (Quartiles and interquartile range)

Set 1 to Set 4

LOWER AND UPPER QUARTILES SHEET 2 Find the lower and upper quartile in each of the sets of data. When you have done that, find the interquartile range. | 1) {2, 7, 4, 2, 3, 6, 11, 9, 14} | | | | | | --- | --- | --- | --- | --- | | order | | | | No. of terms
9 | | Lower Quartile | | Median | | | | Upper Quartile | | Interquartile range | | | | 2) {38, 31, 18, 45, 29, 16, 43, 57, 29, 26, 52} | | | | | | --- | --- | --- | --- | --- | | order | | | | No. of terms | | Lower Quartile | | Median | | | | Upper Quartile | | Interquartile range | | | | 3) {2, 7, 4, 2, 3, 6, 11, 9, 14, 8, 10, 5, 7} | | | | | | --- | --- | --- | --- | --- | | order | | | | No. of terms | | Lower Quartile | | Median | | | | Upper Quartile | | Interquartile range | | | | 4) {4 . 2, 2.8, 1.9, 2.5, 1.4, 3.5, 2. 1, 3.1, 1.9, 2.7} | | | | | | --- | --- | --- | --- | --- | | order | | | | No. of terms | | Lower Quartile | | Median | | | | Upper Quartile | | Interquartile range | | | LOWER AND UPPER QUARTILES SHEET 2 ANSWERS | 1) {2, 7, 4, 2, 3, 6, 11, 9, 14} | | | | | | --- | --- | --- | --- | --- | | order {2, 2, 3, 4, 6, 7, 9, 11, 14} | | | | No. of terms
9 | | Lower Quartile | (2+3)/2 = 2 ½ | Median | 6 | | | Upper Quartile | (9+11)/2 = 10 | Interquartile range | 10 – 2 ½ = 7 ½ | | | 2) {38, 31, 18, 45, 29, 16, 43, 57, 29, 26, 52} | | | | | | --- | --- | --- | --- | --- | | order {16, 18, 26, 29, 29, 31, 38, 43, 45, 52, 57} | | | | No. of terms
11 | | Lower Quartile | 26 | Median | 31 | | | Upper Quartile | 45 | Interquartile range | 45 – 26 = 19 | | | 3) {2, 7, 4, 2, 3, 6, 11, 9, 14, 8, 10, 5, 7} | | | | | | --- | --- | --- | --- | --- | | order {2, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 14} | | | | No. of terms
13 | | Lower Quartile | (3+4)/2 = 3 ½ | Median | 7 | | | Upper Quartile | (9+10)/2 = 4 ½ | Interquartile range | 4 ½ -3 ½ = 1 | | | 4) {4 . 2, 2.8, 1.9, 2.5, 1.4, 3.5, 2. 1, 3.1, 1.9, 2.7} | | | | | | --- | --- | --- | --- | --- | | order {1 .4, 1.9, 1.9, 2. 1, 2.5, 2.7, 2.8, 3.1, 3.5, 4 . 2} | | | | No. of terms
10 | | Lower Quartile | (1.9+1.9)/2 = 1.9 | Median | (2.5+2. 7)/2 = 2.6 | | | Upper Quartile | (3.1+3.5)/2 = 3.3 | Interquartile range | 3.3 – 1.9 = 1.4 | |

FAQs

How do you find the lower quartile and upper quartile for a data set?

First write the data in order. Then use the quartile positions implied by the number of terms to determine the lower quartile and upper quartile, averaging the two middle candidates when needed.

What is the interquartile range (IQR) and how is it calculated?

The interquartile range is the difference between the upper quartile and the lower quartile: IQR = Q3 − Q1.

Do the quartile calculations change when the data set has an even or odd number of terms?

Yes. The worksheets show different handling depending on how the quartile lies between ordered values—sometimes averaging two middle values to get Q1 or Q3.

Oct 22, 2026

Uploaded by Mary Man