Math Problem Statement

Here is a sample data set.

283 299.7 311.8 326.4 335.8 346.2 347.9 354.1 361.1 373.5 380.3 383.2 384.4 384.4 384.4 389.1 389.4 398.8 413.3 417.6 419.3 431.1 451.7 457.7 459.5 459.7 462.2 462.2 462.6 463.1 468.5 468.5 470.2 472.9 482.5 482.9 483.2 490.2 492 497.1 497.1 497.1 505.2 506 507.3 518.7 528.7 531.3 538.9 541.9 543.9 545 546.4 553.5

2 4 6 8 10 12 14 16 18 20 length (cm) 250 300 350 400 450 500 550 600 Frequency [Graphs generated by this script: setBorder(54,40,20,15); initPicture(205,600,0,20);axes(1107,2,1,null,2); fill="blue"; stroke="black"; textabs([165,0],"length (cm)","above");line([250,-0.4],[250,0.4]); text([250,0],"250","below");line([300,-0.4],[300,0.4]); text([300,0],"300","below");line([350,-0.4],[350,0.4]); text([350,0],"350","below");line([400,-0.4],[400,0.4]); text([400,0],"400","below");line([450,-0.4],[450,0.4]); text([450,0],"450","below");line([500,-0.4],[500,0.4]); text([500,0],"500","below");line([550,-0.4],[550,0.4]); text([550,0],"550","below");line([600,-0.4],[600,0.4]); text([600,0],"600","below");textabs([0,115],"Frequency","right",90);rect([250,0],[300,2]);rect([300,0],[350,5]);rect([350,0],[400,11]);rect([400,0],[450,4]);rect([450,0],[500,20]);rect([500,0],[550,11]);rect([550,0],[600,1]);]

Find the first quartile for this data set. Q1 =

Find the third quartile for this data set. Q3 =

Find the interquartile range for this data set. IQR =

Find the lower fence separating outliers from usual values. Fencelow =

Find the upper fence separating outliers from usual values. Fencehigh =

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Quartiles
Interquartile Range
Outliers

Formulas

Q1: The median of the lower half of the data
Q3: The median of the upper half of the data
IQR = Q3 - Q1
Lower Fence = Q1 - 1.5 * IQR
Upper Fence = Q3 + 1.5 * IQR

Theorems

Quartile Theorem: A quartile divides data into four equal parts.
Interquartile Range Theorem: Measures statistical dispersion and outliers.

Suitable Grade Level

Grades 10-12