Chapter 3 Weighted Mean

17.Variance

__________________________________ is the mean of the SQUARED deviations of the mean.

29.Chebyshey's theorem

___________________________________ states that for any set of observations, the proportion of the values that lie within k standard deviations of the mean is at least 1 - (1/k2), where k is any constant greater than 1. K is the number of __________________________________.

31.2.5sqr k2=6.5 1/6.25=.16 c1-.16=84

According to Chebyshev's Theorem at least ______________% of all values are within 2.5 standard deviations of the mean.

25.dollars

If data is measured in dollars, then the computed variance would have units of _________________________________.

9.spread

Measures of dispersion give an idea of the amount of _____________________ in data.

24.standard deviation

If data is measured in units of degrees Fahrenheit, then the computed variance would have units of _______________________________.

8.skew to the right>

If the mean of a data set equals 58, the median equals 21, and the mode equals 8, the distribution is ___________________________(shape).

7.skew to the left<

If the mean of a data set equals 69, the median equals 74, and the mode equals 129, the distribution is ___________________________ (shape).

6.Negitive

In a __________________________ distribution, the mode is larger than the median, and the median is larger than the mean.

4.semetric

In a ___________________________ distribution, the mean, median, and mode are equal.

5.Postive

In a _______________________________________ distribution, the mean is larger than the median, and the median is larger than the mode.

22.population and sample

N represents _______________________ while n represents _____________________.

75, 2

Specifically, Chebyshev's theorem says that at least ______% of all values are within 2 standard deviations of the mean. First ask, what is the value of k, the number of standard deviations? _______

33.

Suppose the average age of a professional employed by a particular computer firm is 28 with a standard deviation of 5 years. Apply Chebyshev's theorem to determine within what range of ages at least 85% of the workers' ages fall.

12. Mean Deviation

The _______________________ measures the mean amount by which the values in a population, or sample, vary from the mean.

11.largest to small

The calculated range is based on ______________ values.

13.MD= e[x--xbar]/N

The formula for mean deviation is:

20.o2= E(x-u)2/N

The formula for population variance is:

21.s2=E(x-U)2/n-1

The formula for sample variance is:

2.-xw= w1x1+w2x2+w3x3/w1+w2+w3=

The formula for the weighted mean is:

10.range 20,30, 40,50,60,70,80 = 60

The mathematical difference in the largest value and smallest value in a data set is called the ______________________.

27.o

The symbol for population standard deviation is ____________.

18.02

The symbol for population variance is _________________.

15.[ ] absoulte value

The | | marks indicate ____________________________.

23.squared

Variance is difficult to interpret because the units are ______________________.

36.294*2 +- 588 of 1365

A company produces a lightweight valve. The weights of the valves produced are normally distributed with a mean weight of 1365 grams and a standard deviation of 294 grams. Within what range would approximately 95% of the valve weights fall? _____________________________

What is the value of k2? ________ What is the value of 1/k2? _____________ What is 1-1/k2? _____________________

2sqr k2= 4 1/4=.75 c 1-.75=.25

1.

A distribution of numbers is approximately bell shaped. If the mean of the numbers is 125 and the standard deviation is 12, between what two numbers would approximately 68% of the values be? Between what two numbers would 95% of the values be? Between what two values would 99.7% of the values be?

32.2.56

According to Chebyshev's Theorem, at least what proportion of the data will be within 1.6 standard deviations of the mean? ______________________

34.

According to Chebyshev's Theorem, how many standard deviations from the mean would include at least 80% of the values?

35.68%,95%,99.7%

The Empirical Rule states that for a symmetrical, bell-shaped curve, at least _________% of the observations will be within 1 standard deviation of the mean; __________% of the observations will be within 2 standard deviations of the mean; and ____________% of the observations will be within 3 standard deviations of the mean.

26.standard deviation

The _______________________________ is the square root of variance.

16.0

The absolute value signs are used when computing mean deviation because without them the sum of the deviations from the mean equals _________________________.

28.s

The symbol for sample standard deviation is __________.

19.S2

The symbol for sample variance is ______________________.

14.sigma adding

The symbol Σ means __________________________.

3.Range large to small, Mean Deviation md=E[x--x]/n varince and standard deviation

The three shapes of distributions are ___________________________, ____________________________, and ____________________________.

2.

The time needed to assemble a particular piece of furniture with experience is normally distributed with a mean time of 43 minutes. If 68% of the assembly times are between 40 and 46 minutes, what is the value of the standard deviation? Suppose 99.7% of the assembly times are between 35 and 51 minutes and the mean is still 43 minutes. What would the value of the standard deviation be now?

1.Several , value

The weighted mean is a special case of the arithmetic mean, it occurs only when there are _______________ observations of the same __________________.