Math Problem Statement

Here is a data set ( ) that has been sorted.

24.5 24.7 25.6 26.1 26.9 27.1 27.1 27.4 27.7 28 28.5 28.6 29.7 31.4 31.5 32.2 32.9 33.3 33.5 33.5 33.6 33.8 33.8 34.1 35.3 35.5 35.5 35.8 35.9 36.4 36.4 36.4 36.6 36.6 36.7 37.1 37.2 37.5 37.7 38.1 38.2 38.8 38.9 38.9 38.9 38.9 39 39.1 39.2 39.4 39.5 39.6 39.8 40 40.2 40.2 40.5 40.6 40.6 40.8 40.8 41.1 41.1 41.5 41.7 41.7 41.8 41.8 42.2 42.2 42.4 42.5 42.5 42.5 42.8 42.8 43.5 44.3 44.7 44.7 44.9 45 45 45.3 45.3 45.4 46 46 46.4 46.6 46.7 48 48.4 48.5 48.7 48.9 48.9 49.5 49.8 50.4 50.4 51.8 51.8 52.2 52.7 52.8 53.9 56.8 58.6

5 10 15 20 25 length (cm) 20 25 30 35 40 45 50 55 60 Frequency [Graphs generated by this script: setBorder(54,40,20,15); initPicture(15.5,60,0,29);axes(117.2,5,1,null,5); fill="blue"; stroke="black"; textabs([165,0],"length (cm)","above");line([20,-0.58],[20,0.58]); text([20,0],"20","below");line([25,-0.58],[25,0.58]); text([25,0],"25","below");line([30,-0.58],[30,0.58]); text([30,0],"30","below");line([35,-0.58],[35,0.58]); text([35,0],"35","below");line([40,-0.58],[40,0.58]); text([40,0],"40","below");line([45,-0.58],[45,0.58]); text([45,0],"45","below");line([50,-0.58],[50,0.58]); text([50,0],"50","below");line([55,-0.58],[55,0.58]); text([55,0],"55","below");line([60,-0.58],[60,0.58]); text([60,0],"60","below");textabs([0,115],"Frequency","right",90);rect([20,0],[25,2]);rect([25,0],[30,11]);rect([30,0],[35,11]);rect([35,0],[40,29]);rect([40,0],[45,28]);rect([45,0],[50,18]);rect([50,0],[55,8]);rect([55,0],[60,2]);]

Use the locator, give the value for the 50-Percentile: P50 =

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Percentiles
Data Analysis

Formulas

P50 position = (n + 1) / 2
P50 = (value at 51st position + value at 52nd position) / 2

Theorems

Percentile Calculation
Median as 50th Percentile

Suitable Grade Level

Grades 9-12