Statistics 230: Chapter 3 Handout 3

***(test) If the coefficient of variation is 40% and the mean is 70, then the variance is equal to _________.

(coefficient of Variation) .4=S/70 } S=28 Answer: S^2=784

The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals __________.

(square root 64) = 8

***Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean would then be_________.

.64=8/(mean)} 12.5

If a data set has an even number of observations, the median is calculated in two steps:

1) put in order 2) take average of middle 2

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is the ________.

Variance

List the four measures of dispersion.

Variance, Standard Deviation, Range, and Inter-quartile Range (IQR)

The mean of a sample is computed by summing ___________ and then dividing by ___________.

values of xi,(and then dividing by).... n

What symbol represents the size of the sample?

n

In computing the mean of a sample, the value of ∑xi is divided by __________

n= sample size

***The variance can never be _________.

negative (cause its a squared term)

The sample variance is always (larger/smaller/the same) as the population variance.

none of these or any (cause it can be larger, smaller, or same)

What are two numerical measures of the linear association between two variables?

Sxy (Covariance) & rxy (Correlation coefficient)

The 75th percentile is referred to as the

3rd Quartile

Since the population size is always larger than the sample size, then the sample statistic is always __________ compared to the population parameter.

>,<, or =

The coefficient of correlation can never be ___________________.

>1 or <1

The heights (in inches) of 25 individuals were recorded and the following statistics were calculated... mean = 70 range = 20 mode = 73 variance = 784 median = 74 The coefficient of variation equals ____________.

CV=28/70*100% = 40%

The median is a measure of _________.

Central Location

Since the mode is the most frequently occurring data value, it is always _________ than the mean.

Greater than or Less than or none

The most important statistical descriptive measure of the Central location of a data set is the _________.

Mean

List the three measures of central location

Mean, Median, and Mode

The value which has half of the observations above it and half the observations below it is called the __________.

Median

What symbol represents the size of the population?

N

The variance of the sample can never be _________.

Negative

The symbol σ2 is used to represent __________ .

Population Variance

The interquartile range is

Q3-Q1

The difference between the largest and the smallest data values is the ___________.

Range

The measure of dispersion that is influenced most by extreme values is the _________.

Range

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals _________.

S= (square root of 576) = 24

The sum of deviations of the individual data elements from their mean is always _______.

Zero

When the data are skewed to the right, the longer tail of the distribution is on the __________.

right