It is known that average house prices today is $371,040 higher compared to 10 years ago and median in the current time also $382,000 higher than house prices 10 years ago.Provide an interpretation of the change of mean and median based on the information above. Compare and contrast these values and comment on the distribution of the increases in house prices. In an attempt to track the increasing house prices in a large city in Australia, a statistician took arandom sample of homes sold this year and another sample of homes sold 10 years ago. Thefollowing set of statistics describe the two sets of data, where the prices are expressed in $000s.MeanMedianModeQ1Q3IQ RangeSDmaxminrange10th percentile90th percentileCoefficient of Variation (%)Current892.44900816816954138100.081146678468756.61025.411.2110 years ago521.45185164845597555.6272040831244859210.67

Given that: Current 10 years ago Mean 892.44 521.4 Median 900 518 Mode 816 516 Q1 816…

Answered: It is known that average house prices…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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It is known that average house prices today is $371,040 higher compared to 10 years ago and median in the current time also $382,000 higher than house prices 10 years ago.

Provide an interpretation of the change of mean and median based on the information above. Compare and contrast these values and comment on the distribution of the increases in house prices.

In an attempt to track the increasing house prices in a large city in Australia, a statistician took a
random sample of homes sold this year and another sample of homes sold 10 years ago. The
following set of statistics describe the two sets of data, where the prices are expressed in $000s.
Mean
Median
Mode
Q1
Q3
IQ Range
SD
max
min
range
10th percentile
90th percentile
Coefficient of Variation (%)
Current
892.44
900
816
816
954
138
100.08
1146
678
468
756.6
1025.4
11.21
10 years ago
521.4
518
516
484
559
75
55.62
720
408
312
448
592
10.67

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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