the median of the set = 12, lowest quartile = 7, highest quartile = 17
in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The median is currently 14, the central datum in an ordered set of 13. Changing 14 to 12 will not satisfy the other requirements. The lowest quartile is the median of the range of the lowest value up to, but not including the median of the whole set, and the highest quartile is the median of the range between the main median and the highest datum, excluding the main median. An alternative method of including the main median in the two sets making the size of the two sets 7 instead of 6, means that one of the central values, required to be 7 and 17, must already exist in the set and, since neither does and we can only change one datum, we cannot use this method.

Because the size of the dataset is 13 the median splits the data into two sets of 6 data, either side of the median. The current value of 12 needs to be "pushed" one place to the right to become the median of the dataset. This will happen if a datum higher than 12 is made lower than 12.

Let X1, X2, X3, ..., X13 be the data values. The median (Q2) is X7=12 in the required dataset. X3 and X4 are the central two values of the lowest quartile and X10 and X11 are the central two values of the highest quartile. There are two ways of calculating X3 and X4, and X10 and X11. The Q1=(1/2)(X3+X4)=7 or Q1=(1/4)(X3+3X4)=7 and Q3=(1/2)(X10+X11)=17 or Q3=(1/4)(X10+3X11). So if X3=6 and X4=8, then Q1=7; similarly if X10=16 and X11=18, then Q3=17. So if the current X12 or X13 is changed so that it in the ordered set it becomes X1 or X2<6, then all conditions will be met. For example, if current X13 is changed from 24 to 5 then the ordered dataset is 3 5 6 8 9 10 12 14 15 16 18 19 20, and Q1=7, Q2=12, Q3=17.

If the alternative method for calculating Q1 and Q3 is used we would have Q1=(1/4)(6+24)=7.5 and Q2=(1/4)(16+54)=17.5, which clearly does not fit the requirements.

by Top Rated User (1.1m points)

Related questions

2 answers
asked Oct 24, 2012 in Calculus Answers by anonymous | 649 views
1 answer
asked Oct 10, 2012 in Statistics Answers by anonymous | 576 views
1 answer
asked May 7, 2020 in Other Math Topics by doogie | 506 views
1 answer
asked Jan 27, 2013 in Algebra 1 Answers by anonymous | 721 views
1 answer
1 answer
asked Feb 21, 2013 in Pre-Algebra Answers by anonymous | 481 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,938 users