MEAN CALCULATOR : ICSE AND CBSE ( Assumed and Step-Deviation Method)

 MEAN CALCULATOR : ICSE AND CBSE ( Direct, Assumed and Step-Deviation Method)

Calculation of mean using python programming.

Mean Formula For Grouped Data

There are three methods to find the mean for grouped data, depending on the size of the data. They are:

• Direct Method
• Assumed Mean Method
• Step-deviation Method

Let us go through the formulas in these three methods given below:

Direct Method

Suppose x1, x2, x3,…., xn be n observations with respective frequencies f1, f2, f3,…., fn. This means, the observation x1 occurs f1 times, x2 occurs f2 times, x3 occurs f3 times and so on. Hence, the formula to calculate the mean in the direct method is:

$\begin{array}{l}\bar{x}=\frac{f_1{x}_1+f_2{x}_2+f_3{x}_3+\dots .+f_n{x}_n}{f_1+f_2+f_3+\dots .+f_n}\end{array}$

Or

$\begin{array}{l}\bar{x}=\frac{\sum _{i=1}^n{f}_i{x}_i}{\sum _{i=1}^n{f}_i}\end{array}$

Here,

∑fixi = Sum of all the observations

∑fi = Sum of frequencies or observations

This method is used when the number of observations is small.

Assumed Mean Method

In this method, we generally assume a value as the mean (namely a). This value is taken for calculating the deviations based on which the formula is defined. Also, the data will be in the form of a frequency distribution table with classes. Thus, the formula to find the mean in assumed mean method is:

$\begin{array}{l}Mean,(\bar{x})=a+\frac{\sum f_i{d}_i}{\sum f_i}\end{array}$

Here,

a = assumed mean

fi = frequency of ith class

di = xi – a = deviation of ith class

Σfi = N = Total number of observations

xi = class mark = (upper class limit + lower class limit)/2

Click here to learn more about the assumed mean method in detail.

Step-deviation Method

When the data values are large, the step-deviation method is used to find the mean. The formula is given by:

$\begin{array}{l}Mean,(\bar{x})=a+h\frac{\sum f_i{u}_i}{\sum f_i}\end{array}$

Here,

a = assumed mean

fi = frequency of ith class

xi – a = deviation of ith class

ui = (xi – a)/h

Σfi = N = Total number of observations

xi = class mark = (upper class limit + lower class limit)/2

Run the program on Google Colab 

def parityString(string):

        while len(string) < 9:

            string += " "

        return string

def stepDeviationMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass):

    classWidth = upperLimitOfFirstClass - lowerLimitOfFirstClass

    listLowerClassLimits = []

    listUpperClassLimits = []

    classFrequency = []

    midValue = []

    assumed_Mean = 0

    for i in range(numberOFClasses):

        listLowerClassLimits.append(lowerLimitOfFirstClass)

        listUpperClassLimits.append(upperLimitOfFirstClass)

        print("Enter the frequency of the class:",listLowerClassLimits[i],"-",listUpperClassLimits[i])

        classFrequency.append(float(input()))

        midValue.append((lowerLimitOfFirstClass+upperLimitOfFirstClass)/2.0)

        lowerLimitOfFirstClass += classWidth

        upperLimitOfFirstClass += classWidth

    print("Select the assumed mean (A) from the following values:",midValue)

    assumed_Mean = float(input())

    di = []

    fidi = []

    sum_fi = 0

    sum_fidi = 0

    print(parityString("CLASSES"),parityString("frequency(fi)"),parityString("mid value(xi)"),"   ",parityString("di=(xi-A)/h"),end='')

    print("  ",parityString("fi*di"))

    for i in range(numberOFClasses):

        di.append((midValue[i]-assumed_Mean)/classWidth)

        fidi.append(classFrequency[i]*di[i])

        print(str(listLowerClassLimits[i]),end =' '),

        print("-",parityString(str(listUpperClassLimits[i])),"   ",end='')

        print(parityString(str(classFrequency[i])),"  ",parityString(str(midValue[i])),"  ",parityString(str(di[i])),end = ' ')

        print(parityString(str(fidi[i])))

        sum_fi += classFrequency[i]

        sum_fidi += fidi[i]

    print("--------------------------------------------------------------------------------------------")

    print("Assumed mean A =",assumed_Mean," Class width h = ",classWidth)

    print(parityString("fi="+str(sum_fi)),parityString(" "),"   ",parityString("fidi="+str(sum_fidi)))

    print("CALCULATED MEAN BY SHORT-CUT METHOD:",round(assumed_Mean+(sum_fidi/sum_fi)*classWidth,2))

    print()

def shortCutMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass):

    classWidth = upperLimitOfFirstClass - lowerLimitOfFirstClass

    listLowerClassLimits = []

    listUpperClassLimits = []

    classFrequency = []

    midValue = []

    assumed_Mean = 0

    for i in range(numberOFClasses):

        listLowerClassLimits.append(lowerLimitOfFirstClass)

        listUpperClassLimits.append(upperLimitOfFirstClass)

        print("Enter the frequency of the class:",listLowerClassLimits[i],"-",listUpperClassLimits[i])

        classFrequency.append(float(input()))

        midValue.append((lowerLimitOfFirstClass+upperLimitOfFirstClass)/2.0)

        lowerLimitOfFirstClass += classWidth

        upperLimitOfFirstClass += classWidth

    print("Select the assumed mean (A) from the following values:",midValue)

    assumed_Mean = float(input())

    di = []

    fidi = []

    sum_fi = 0

    sum_fidi = 0

    print(parityString("CLASSES"),parityString("frequency(fi)"),parityString("mid value(xi)"),"   ",parityString("di=xi-A"),end='')

    print(parityString("fi*di"))

    for i in range(numberOFClasses):

        di.append(midValue[i]-assumed_Mean)

        fidi.append(classFrequency[i]*di[i])

        print(str(listLowerClassLimits[i]),end =' '),

        print("-",parityString(str(listUpperClassLimits[i])),"   ",end='')

        print(parityString(str(classFrequency[i])),"  ",parityString(str(midValue[i])),"  ",parityString(str(di[i])),end = ' ')

        print(parityString(str(fidi[i])))

        sum_fi += classFrequency[i]

        sum_fidi += fidi[i]

    print("--------------------------------------------------------------------------------------------")

    print("Assumed mean A =",assumed_Mean)

    print(parityString("fi="+str(sum_fi)),parityString(" "),"   ",parityString("fidi="+str(sum_fidi)))

    print("CALCULATED MEAN BY SHORT-CUT METHOD:",round(assumed_Mean+(sum_fidi/sum_fi),2))

    print()

def directMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass):

    classWidth = upperLimitOfFirstClass - lowerLimitOfFirstClass

    listLowerClassLimits = []

    listUpperClassLimits = []

    classFrequency = []

    midValue = []

    for i in range(numberOFClasses):

        listLowerClassLimits.append(lowerLimitOfFirstClass)

        listUpperClassLimits.append(upperLimitOfFirstClass)

        print("Enter the frequency of the class:",listLowerClassLimits[i],"-",listUpperClassLimits[i])

        classFrequency.append(float(input()))

        midValue.append((lowerLimitOfFirstClass+upperLimitOfFirstClass)/2.0)

        lowerLimitOfFirstClass += classWidth

        upperLimitOfFirstClass += classWidth

    fixi = []

    sum_fi = 0

    sum_fixi = 0

    print(parityString("CLASSES"),parityString("frequency(fi)"),parityString("mid value(xi)"),"   ",parityString("fi*xi"))

    print()

    for i in range(numberOFClasses):

        fixi.append(classFrequency[i]*midValue[i])

        print(str(listLowerClassLimits[i]),end =' '),

        print("-",parityString(str(listUpperClassLimits[i])),"   ",end='')

        print(parityString(str(classFrequency[i])),"  ",parityString(str(midValue[i])),"  ",parityString(str(fixi[i])))

        sum_fi += classFrequency[i]

        sum_fixi += fixi[i]

    print("--------------------------------------------------------------------------------------------")

    print(parityString(" "),parityString("fi="+str(sum_fi)),parityString(" "),"   ",parityString("fixi="+str(sum_fixi)))

    print("CALCULATED MEAN BY DIRECT METHOD:",round(sum_fixi/sum_fi,2))

print("****** MEAN CALCULATION *******")

key = 0

while key != -99:

    print(" WELCOME TO THE MAIN MENU ***** MEAN CALCULATION FOR CONTINUOUS DATA *****")

    print(" Press 1 to CALCULATE MEAN BY DIRECT METHOD: ")

    print(" Press 2 to CALCULATE MEAN BY SHORT CUT METHOD / ASSUMED MEAN METHOD: ")

    print(" Press 3 to CALCULATE MEAN BY STEP DEVIATION METHOD: ")

    print(" Type -99 to exit the menu:")

    key = int(input("Enter your choice:"))

    if key == 1:

        numberOFClasses = int(input("Enter the number of classes:"))

        lowerLimitOfFirstClass = int(input("Enter the lower limit of the first classes:"))

        upperLimitOfFirstClass = int(input("Enter the upper limit of the first classes:"))

        directMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass)

    if key == 2:

        numberOFClasses = int(input("Enter the number of classes:"))

        lowerLimitOfFirstClass = int(input("Enter the lower limit of the first classes:"))

        upperLimitOfFirstClass = int(input("Enter the upper limit of the first classes:"))

        shortCutMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass)

    if key == 3:

        numberOFClasses = int(input("Enter the number of classes:"))

        lowerLimitOfFirstClass = int(input("Enter the lower limit of the first classes:"))

        upperLimitOfFirstClass = int(input("Enter the upper limit of the first classes:"))

        stepDeviationMethod(numberOFClasses,lowerLimitOfFirstClass,upperLimitOfFirstClass)

    if key == -99:

        print("Exited from main menu:")