Answered: a) Find the Mean Score for the…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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a) Find the Mean Score for the Statistics Quiz (X), and the Mean for the Math Quiz (Y) b) Use the pooled (weighted) mean formula to find the pooled (weighted) mean for the Math Quiz scores given above, and another section of 6 students who had a mean score or 10

x= 3,7,5

y=10,22,16

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 + ...

Expert Solution

Step 1

Given : Score for the Statistics Quiz (X), and the score for the Math Quiz (Y) is provided .

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$M e a n = \frac{S u m o f t e r m s}{N u m b e r o f t e r m s}$

Statistics Quiz (X) :

Sum of terms = 3 + 7 + 5 = 15

Number of terms = 3

$M e a n = \frac{S u m o f t e r m s}{N u m b e r o f t e r m s}$

= $\frac{15}{3}$

Mean = 5

Math Quiz (Y) :

Sum of terms = 10 + 22 +16 = 48

Number of terms = 3

$M e a n = \frac{S u m o f t e r m s}{N u m b e r o f t e r m s}$

= $\frac{48}{3}$

Mean = 16

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a) Find the Mean Score for the Statistics Quiz (X), and the Mean for the Math Quiz (Y) b) Use the pooled (weighted) mean formula to find the pooled (weighted) mean for the Math Quiz scores given above, and another section of 6 students who had a mean score or 10 x= 3,7,5 y=10,22,16