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Chapter 4

Comprehensive index

Comprehensive index

From its roles and the angle of the method characteristics,comprehensive index can be summarized into three categories:

The conception and function of total amount index

- Total amount index is social economic phenomenon must reflect the time, the place, the total scale, under the condition of the level of statistics.
- Total amount index form is JueDuiShu, may also display to absolute difference.

Effect:

- Total amount index can reflect a country's basic national conditions and National strength, reflect a department, unit and so on human, financial,The basic data of the content.
- Total amount index is making decisions and the basis of scientific management.
- Total amount index is the the foundation of calculated relative index and average index.

Total amount index calculation

- Calculation principle:
- 1. The phenomenon of similar nature.
- 2. Clear statistical meaning.
- 3. Measurement unit shall be consistent.

The concept of relative index

- Opposite index is two contact index, the result of the numerical contrast reflects the number of things characteristics and quantity

Opposite index role

- Can the specific social and economic phenomenon that the proportion between the relationship.
- Can make some can't direct comparison to find out the things together the basis of comparison
- Opposite index is easy to remember, easy to confidential

Structure relative index

- 1. Can reflect the overall the internal structure of the features
- 2. Through the different period of relative change, we can see that the changes of things process and its development trend
- 3. Can reflect on the human, material and financial resources utilization degree and the production and business operation effect quality
- 4. Structure in the application of the relative average

Measures of Central Tendency

Mean

Arithmetic average

Sum of all data values divided by the number of data values within the array

Most frequently used measure of central tendency

Strongly influenced by outliers- very large or very small values

Measures of Central Tendency

Median

Data value that divides a data array into two equal groups

Data values must be ordered from lowest to highest

Useful in situations with skewed data and outliers (e.g., wealth management)

Measures of Central Tendency

Determine the median value of

48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

Organize the data array from lowest to highest value.

59, 60, 62, 63, 63

58,

2, 5, 48, 49, 55,

Select the data value that splits the data set evenly.

Median = 58

What if the data array had an even number of values?

60, 62, 63, 63

58, 59,

5, 48, 49, 55,

Measures of central tendency

Usually the highest point of curve

Mode

Most frequently occurring response within a data array

May not be typical

May not exist at all

Mode, bimodal, and multimodal

Measures of Central Tendency

Determine the mode of

48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

Mode = 63

Determine the mode of

48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55

Mode = 63 & 59 Bimodal

Determine the mode of

48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55

Mode = 63, 59, & 48 Multimodal

Data Variation

Measure of data scatter

Range

Difference between the lowest and highest data value

Standard Deviation

Square root of the variance

Variance

Average of squared differences between each data value and the mean

Range

Calculate by subtracting the lowest value from the highest value.

Calculate the range for the data array.

2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

Standard Deviation

- Calculate the mean .
- Subtract the mean from each value.
- Square each difference.
- Sum all squared differences.
- Divide the summation by the number of values in the array minus 1.
- Calculate the square root of the product.

Standard Deviation

Calculate the standard deviation for the data array.

2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

1.

2.

2 - 47.64 = -45.64

5 - 47.64 = -42.64

48 - 47.64 = 0.36

49 - 47.64 = 1.36

55 - 47.64 = 7.36

58 - 47.64 = 10.36

59 - 47.64 = 11.36

60 - 47.64 = 12.36

62 - 47.64 = 14.36

63 - 47.64 = 15.36

63 - 47.64 = 15.36

Standard Deviation

Calculate the standard deviation for the data array.

2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

3.

11.362 = 129.05

12.362 = 152.77

14.362 = 206.21

15.362 = 235.93

15.362 = 235.93

-45.642 = 2083.01

-42.642 = 1818.17

0.362 = 0.13

1.362 = 1.85

7.362 = 54.17

10.362 = 107.33

Standard Deviation

Calculate the standard deviation for the data array.

2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

4.

2083.01 + 1818.17 + 0.13 + 1.85 + 54.17 + 107.33 + 129.05 + 152.77 + 206.21 + 235.93 + 235.93

= 5,024.55

7.

5.

11-1 = 10

6.

S = 22.42

Variance

Average of the square of the deviations

- Calculate the mean.
- Subtract the mean from each value.
- Square each difference.
- Sum all squared differences.
- Divide the summation by the number of values in the array minus 1.

Graphing Frequency Distribution

Numerical assignment of each outcome of a chance experiment

A coin is tossed 3 times. Assign the variable X to represent the frequency of heads occurring in each toss.

HHH

X =1 when?

3

HHT

2

HTT,THT,TTH

2

HTH

THH

2

1

HTT

THT

1

TTH

1

0

TTT

Graphing Frequency Distribution

The calculated likelihood that an outcome variable will occur within an experiment

HHH

3

0

HHT

2

2

HTH

1

THH

2

1

HTT

2

THT

1

TTH

1

3

0

TTT

Histogram

Open airplane passenger seats one week before departure

What information does the histogram provide the airline carriers?

What information does the histogram provide prospective customers?

Measures of Central Tendency

Median

Data value that divides a data array into two equal groups

Data values must be ordered from lowest to highest

Useful in situations with skewed data and outliers (e.g., wealth management)

Measures of Central Tendency

Determine the median value of

48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

Organize the data array from lowest to highest value.

58,

59, 60, 62, 63, 63

2, 5, 48, 49, 55,

Select the data value that splits the data set evenly.

Median = 58

What if the data array had an even number of values?

60, 62, 63, 63

58, 59,

5, 48, 49, 55,

Measures of central tendency

Usually the highest point of curve

Mode

Most frequently occurring response within a data array

May not be typical

May not exist at all

Mode, bimodal, and multimodal

Measures of Central Tendency

Determine the mode of

48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

Mode = 63

Determine the mode of

48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55

Mode = 63 & 59 Bimodal

Determine the mode of

48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55

Mode = 63, 59, & 48 Multimodal

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