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BA201 and BA321

Descriptive Measures: Excel and Equations

Excel- commands used in this topic in Office 97 and Office 2000

§ Equations §

Sample Mean

Descriptive Measures

Equations

§ Sum of Deviations § Sample Mean § Population Mean §

§ Median § Range § Sum of the Squared Deviations §

§ Variance § Standard Deviation § Empirical Rule §

§ Z Score § Other Equations not found at this topic site §

Equations found at this topic site:

1.  Sum of Deviations

Sd = S(x - xbar) = 0

xbar = Sx / n =

S means sum

x = data value

n = number of data values in sample

m = Sx / N

S means sum

x = data value

N = number of data values in the population

Md = (n + 1) / 2 position in order array (find data value in that position)

(b) When n is even,

Md = (two middle values) / 2

5. Range

= high data value - low value

R = H - L

6.  Sum of the Squared Deviations

Sd² = S(x - xbar)²

d² = (individual deviation) ²

x = data value

xbar = sample mean =

s² = Sd² / (n - 1) = S(x - xbar)² / (n - 1)

(not for hand calculations)

S means sum

d² = (individual deviation)² = (x - xbar)²

n = number of data values in sample

xbar = Sx / n = sample mean =

s² = S(x - m)² / N

S means sum

x = data value

m = Sx / N = population mean

N = number of data values in population

s² = [Sx² - (Sx)² / n] / (n - 1) (use for hand calculations)

n = number of data values in sample

Sample s = Ö[s²] = Ö[Sd² / (n - 1)]

= Ö[S(x - xbar)² / (n - 1)]

(not for hand calculations)

Ö = square root

S means sum

d² = (individual deviation)² = (x - xbar)²

n = number of data values in sample

xbar = Sx / n = sample mean =

x = data value

(n - 1) = degrees of freedom

(b) Computing Formula Sample Standard Deviation

s = Ös² = Ö{[Sx² - (Sx)² / n] / (n - 1)}

(use for hand calculations)

n = number of data values in sample

10. Z Score

Z = [x - xbar] / s

x = data value

xbar = mean (sample) =

[x - xbar] = individual deviation

s = standard deviation (the average deviation)

§ Midrange § Mean Absolute Deviation §

§ Coefficient of Variation §

§  Percentile § Interquartile Range §

§ Pearsonian Coefficient of Skewness §

§ Chebyshev's Inequality §

§ Grouped Data § Coding Data §

1. Midrange

Mr = the average of the lowest (L)

and highest (H) data values.

Mr = [(L) + (H)] / 2

S means sum

x = data value

xbar = Sx / n = sample mean =

n = number of data values in sample

3. Coefficient of Variation

CV = [s / xbar]100

s = sample standard deviation

xbar = sample mean =

% = the percentile

n = number of data

P(%) = position in ordered array

5. Interquartile range

IQR = 3rd Quartile - 1st Quartile

6. Pearsonian coefficient of skewness-

Sk = 3[xbar - Md] / s

xbar = sample mean =

Md = median

s = sample standard deviation

7. Chebyshev's Inequality-

(a) At least 75% of data values between xbar ± 2s

(b) At least 89% of data values between xbar ± 3s

xbar = sample mean =

s = sample standard deviation

8. Approximating statistics from grouped data

(a) Sample Mean, xbar =

xbar » [Sf(m)] / n,

f is the class frequency

m is the class midpoint

n is the sample size

f is the class frequency

m is the class midpoint

n is the sample size

10. Coding Data Values

(a) Rules for Subtraction and Addition of C:

(1) If C subtracted from original data:

actual xbar = xbar_adj + C

S_adj = actual S

(2) If C added from original data:

actual xbar = xbar_adj - C

S_adj = actual S

(b) Rules for Multiplication and Division by C:

(1) If C divided into original data:

actual xbar = [xbar_adj ] [ C ]

actual S = [S_adj ] [C]

(2) If original data multiplied by C:

actual xbar = [xbar_adj ] / [ C ]

actual S = [S_adj ] / [C]

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ALL RIGHTS RESERVED Dr. James V. Pinto