Finding the Median Salary

Difficulty: Hard · Topics: Probability, Statistics, Box Plots

The box plot summarises the monthly salaries of 6 people.

graph "x":[-0.6,13.68],"y":[-1.7,2.2],"axes":false,"label":"Box plot of six salaries: minimum 850, Q1 1000, median A, Q3 2000, maximum 2300","items":["type":"line","from":[0.0,1.2],"to":[1.034,1.2],"ink":true,"type":"line","from":[7.931,1.2],"to":[10.0,1.2],"ink":true,"type":"line","from":[0.0,0.95],"to":[0.0,1.45],"ink":true,"type":"line","from":[10.0,0.95],"to":[10.0,1.45],"ink":true,"type":"polygon","points":[[1.034,0.78],[7.931,0.78],[7.931,1.6199999999999999],[1.034,1.6199999999999999]],"fill":0.25,"ink":false,"type":"line","from":[3.966,0.78],"to":[3.966,1.6199999999999999],"ink":false,"width":2.6,"type":"line","from":[0.0,0.95],"to":[0.0,0],"dash":true,"ink":true,"width":0.8,"type":"line","from":[1.034,0.75],"to":[1.034,0],"dash":true,"ink":true,"width":0.8,"type":"line","from":[3.966,0.75],"to":[3.966,0],"dash":true,"ink":true,"width":0.8,"type":"line","from":[7.931,0.75],"to":[7.931,0],"dash":true,"ink":true,"width":0.8,"type":"line","from":[10.0,0.95],"to":[10.0,0],"dash":true,"ink":true,"width":0.8,"type":"line","from":[-0.2,0],"to":[10.8,0],"ink":true,"end":"arrow","type":"label","at":[0.0,-0.65],"text":"850","italic":false,"type":"label","at":[1.034,-1.25],"text":"1000","italic":false,"type":"label","at":[3.966,-0.65],"text":"A","italic":false,"type":"label","at":[7.931,-0.65],"text":"2000","italic":false,"type":"label","at":[10.0,-0.65],"text":"2300","italic":false,"type":"label","at":[11.0,0.2],"text":"Salary","anchor":"e","italic":false]

The mean of the six salaries is 1500. Find A.

(Quartiles are the medians of the lower and upper halves of the ordered data, not counting the median itself.)