Bus102 statistics chapter 3

Question 1

what does measures of location mean ?

Answer 1

A measure of location is a value used to describe the central tendency of a set of data.

Question 2

what are the three common measures?

Answer 2

1. mean
2. median
3. mode

Question 3

what is the Arithmetic mean?

Answer 3

The arithmetic mean is the most widely reported measure of location .

Question 4

what is population mean?

Answer 4

The population mean is an average of a group characteristic.

A measurable characteristic of a population is a parameter.

Question 5

what does Parameter mean?

Answer 5

A characteristics of a population.

Question 6

what is sample mean ?

Answer 6

The sample mean is an average value found in a sample.

A measurable characteristic of a sample is a statistics.

Question 7

Properties of Arithmetic mean = sample mean :

Answer 7

1. Interval or ratio scale of measurement is required.
2. All the data values are used in the calculation ,
3. It is unique.
4. The sum of the deviations from the mean equals zero.
5. A weakness of the mean is that it is affected by extreme values .

The sum of the deviations from the mean equals zero.
how it is equal zero?
Ex: x bar =3 1,2,3,4,5
xI -xbar I-3= -2 2-3= - I 3-3=0 4-3= I 5-3=2-2+-I+0+I+2=0

Question 8

what does median mean?

Answer 8

The midpoint of the values after they have been ordered from the minimum to the maximum values .

Ex: minimum to maximum :

$60,000 X
$65,000 X
$70,000   median 
$80,000  X
$275,000 X

the median is $70,000.

Question 9

Characteristics of the median :

Answer 9

1. The median is the value in the middle of a set of ordered data.
2. At least the ordinal scale of measurement is required.
3. It is not influenced by extreme values.
4. Fifty percent of the observations are larger than the median.
5. It is unique to a set of data.

Ex:
2,4,5,6,7,8
Median: 5+6 /2 = 11/2=5.5

Question 10

How to Find the median ?

Answer 10

1. To find the median for an even numbered data set sort the observations and calculate the average of the two middle values .

Ex;
The number of hours a sample of 10 adults used Facebook last month:
3,5,7,9,1,3,9,17,10
arrange the data in ascending order gives:
Minimum to maximum: 1,3,3,5,5,7,9,9,10,17
x x x x x x x x
Median: 5+7/2=12/2=6.

Question 11

what does mode mean?

Answer 11

The value of the observation that occurs most frequently.

Question 12

Characteristics of the mode:

Answer 12

1. The mode can be found for nominal level data.

2. A set of data can have more than one mode.

Question 13

what is the weighted mean?

Answer 13

The weighted mean is found by multiplying each observation ,x ,by its corresponding weight ,w.

Question 14

what is the Geometric mean ?

Answer 14

The geometric mean is the nth root of the product of n positive values .

Question 15

why study Dispersion?

Answer 15

1. The dispersion is the variation or spread in a set of data .

Question 16

what is the range?

Answer 16

The range is the difference between the maximum and minimum values in a set of data.

The formula of range:
Range = maximum value - minimum value .

Question 17

The major characteristics of the range :

Answer 17

1. Only two values are used in its calculation.
2. It is influenced by extreme values.
3. It is easy to compute and to understand.

Question 18

what is population variance?

Answer 18

Population variance (σ2) tells us how data points in a specific population are spread out. It is the average of the distances from each data point in the population to the mean, squared.

Major characteristics of the variance are:

1. All observations are used in the calculation .
2. The units are somewhat difficult to work with, they are the original units squared.

Question 19

What is sample variance?

Answer 19

The sample variance, s2, is used to calculate how varied a sample is.

Question 20

what is standard deviation?

Answer 20

A measure of the dispersion or variation of a set of data values.

The major characteristics of the standard deviation are:

1. It is in the same units as the original data .
2. It is the square root of the average squared distance from the mean.
3. It cannot be negative.
4. It is the most widely used measure of dispersion.

Question 21

what is Chebyshev’s Theorem?

Answer 21

Chebyshev’s Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.

Question 22

what is the Empirical Rule?

Answer 22

the empirical rule states that 99.7% of data occurs within three standard deviations of the mean within a normal distribution. To this end, 68% of the observed data will occur within the first standard deviation, 95% will take place in the second deviation, and 97.5% within the third standard deviation. The empirical rule predicts the probability distribution for a set of outcomes.