I need help with this question
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

If you have a certain number n numerical data values arranged in order from least to greatest, then the median is the central value if n is odd, or it's the average of the two central values if n is even. That tells us where the 12 is in the dataset. 

If you add all the data values in the set then divide by n the answer is the mean 11. Another way of looking at this is the total sum of all data values is 11n. 

The mode is 8, which means that the value 8 appears more than once in the dataset, and also means that if other data values are also repeated, then 8 is repeated the most.

A range of 10 means that the difference between the smallest and largest data values is 10.

Can we find examples of datasets meeting the requirements? To answer this, let's consider the range. If the lowest data value is X1 then the highest is Xn=X1+10. X1<8 (otherwise X1 could not be the lowest data value) and Xn>12, the median. So X1+10>12, and X1>2, therefore 2<X1<8.

Now consider n: first consider n is odd, so that the median 12 is the central value. n≥7 because the minimum arrangement would be X1,8,8,12,...,...,X7.

Take n=7. If the mean is 11, then the sum of the data=77. This gives us a clue about X5 and X6, which can be represented by 12+xand 12+x6 because both data values must be greater than the median. However, these data values must also be less than X7. So we have 12+xi<X7 where i is 6 or 7. The total sum of the data values is 2X1+38+24+x5+x6=77. Therefore:

2X1+x5+x6=15. But 2<X1<8, so x5+x6=15-2X1. The RHS has a range of values: (-1,11). Since x5 and x6 must be positive, this range is limited to (0,11) corresponding to (7.5,2) for X1 and (17.5,12) for Xn. For example, if X1=7, x5+x6=1, so, since x6>x5, x6>0.5 and x5<0.5. Suppose x5=0.4 and x6=0.6 then we would have 7,8,8,12,12.4,12.6,17, which has a mean of 11, a median of 12, a mode of 8, and a range of 10.

Another example: X1=6, x5+x6=3, let x5=1.4 and x6=1.6. Dataset is 6,8,8,12,13.4,13.6,16. Note that the gap between X6 and X7 is decreasing.

When X1=5, x5+x6=5. Let x5=2.4 and x6=2.6. Dataset is 5,8,8,12,14.4,14.6,15. Now the gap between X6 and X7 narrows further. 

The minimum value of X1 is determined by the inequality: 12+½(15-2X1)<10+X1, 24+15-2X1<20+2X1, 19<4X1, X1>19/4 or X1>4.75. The valid range for Xis therefore (4.75,7.5) when n=7.

by Top Rated User (1.1m points)

Related questions

1 answer
asked Mar 13, 2013 in Pre-Algebra Answers by anonymous | 2.8k views
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
16,939 users