1. Descriptive statistics using Excel
Displaying Data
Calculating Measures of Central Tendency and Dispersion
Classification of data
Index Numbers and Correlation
Bell Shaped distribution
Kari Peisa, Ramk/Teli 2006

2. Displaying Data Types of Data and Measurement Scales Scale Data
Kvalitative
Kvantitative
Nominal X
Ordinal
Interval
Ratio

3. Constructing Diagrams in Excel
General instructions
1. Construct an array where data values form continues series either in rows or in columns
2. Write titles for each series
3. Paint (=activate) the series which you want to include in diagram (data + titles), select Chart Wizard, and follow the instructions

4. Examples of Displaying Data Nominal Scale and Pie Chart
Observations can be assigned to different categories which can’t be placed in a meaningful order

5. Examples of Displaying Data Ordinal Scale and Bar Chart
Classes can be rank-ordered from highest to lowest.
Classes may be represented also numerically when the measures of central tendency have a real value. But, do they actually have a real meaning?

6. Examples of Displaying Data Interval Scale and Line Chart
Addition and subtraction but not multiplication or division can be performed on data to compare observations. We can say that temperature at 15:00 is 1.1 C warmer than at 12:00, but we can’t say for example that -6C is twice as warm as -12 C or vice versa.

7. Examples of Displaying Data Ratio Scale and Line Chart
Ratio data has an absolute beginning point (true 0 point).
All mathematical operations can be performed to compare values. We can say that the length of the plant in Septemper is more than twice as tall as in June.

8. Measures of Central Tendency
Average (Mean)
Mode
Median
Quartiles and Percentiles
The most frequently occurred
The occurrence in the middle of a set of ordered occurrences
The occurrence at the first (25%), second (50%) or third (75%) quartile or at the given percentile (p %) of a set of ordered occurrences

9. Measures of Central Tendency in Excel
Average (Mean)
Write the formula
into a cell …
=AVERAGE(B2:E5) =
=AVERAGE(A1:A4;B2;C1:C2;E1:E4)
A colon (:) stands between the upper left corner and the lower right corner of an array
Empty cells don’t effect on the value of mean
The reference to an array is made by painting the array
The semicolon (;) connects separate arrays

10. Measures of Central Tendency in Excel
Or, use the wizard: Insert function…
Select
Category: Statistics
Function: Average
Activate the command line in the box and paint an array in Excel sheet

11. Measures of Central Tendency in Excel
Mode
Median
Quartiles
Percentiles
=MODE(B2:B5;D2:E4)
1., 2. or 3. quartile
(the 2. = Median)
=MEDIAN(B2:B5;D2:E4)
=QUARTILE((B2:B5;D2:E4);1)
=PERCENTILE((B2:B5;D2:E4);0.35))

12. Measures of Dispersion
Average deviation
Variance
Standard Deviation
Skewness
Skewness characterizes the degree of asymmetry of a distribution around its mean. It has been formulated in many ways.
Pearson:

13. Measures of Dispersion in Excel
Average deviation
Variance
Standard Deviation
Skewness
=AVEDEV(B2:B5;D2:E4)
=VAR(B2:B5;D2:E4)
=STDEV(B2:B5;D2:E4)
=SKEW(B2:B5;D2:E4)

14. Classification (Grouping) of Data
In classification we arrange a large sample of data into classes
There are some rules usually followed when arranging classes
The classes should be of equal size (if possible)
All data values from the original table need to be included in one and only in one class
The number of classes should be between 5 and 15.

15. Classification in Excel
The frequencies indicate the number of observations in the data array that are more than the upper limit in the previous row but less than or equal to the upper limit in this row
Activate the (whole) frequency column and write the formula
=FREQUENCY(data;bins)
into the first cell.
Remark! This is an array formula, which means that we have to accept the formula by pressing:
shift + ctrl + enter

16. Index Numbers
Index numbers are used to display data in proportional form
Source: CIA/ World Factbook 2002

17. Writing own formulas in Excel
Fill right the formula
Formula:
=C2/$B$2*$B$6
Some fundamental rules for writing formulas
Starts with = sign
A pair ColumnRow refers a cell in a relative position
A pair $Column$Row refers a cell in an absolute position
In arrays you should be able to fill right or fill down formulas that are correctly formed
Press F4 for switching between relative, absolute, and mixed references

18. Displaying Correlation in Scattered Chart
In scattered chart two data series are displayed in correspondence. The correlation coefficient between two measurement variables and different fitted curves are associated with this type of chart.

19. Bell-Shaped model
When the sample size is reasonably large and tha data are not too skewed, we can estimate the real distribution by a mathematical model called ”bell-shaped” model (or Gaussian shape or Normal Distribution).
The model needs to know the mean and the standard deviation of the original data

20. Example of using Bell-Shaped Model
How many percentage of the students in the previous frequency distribution got the mark at least 4?
From original data:
With the bell-shaped model, where the average =2.697 and standard deviation = of the original data, we have to calculate the total area under the model curve after the point x=3.5
In Excel the formula is
And it returns 0.246
=1-NORMDIST(3.5;2.697;1.1677;1)
Total area = 1
Returns the area before x=3.5