$CATEGORY: Maths - TicTacLearn/13. Statistics/13. Statistics--Mean of Grouped Data

//Multiple Choice

What is the purpose of the step deviation method? {
= To reduce errors in calculations
~ To find the range of the data
~ To calculate the mode
~ To eliminate the need for midpoints
}

In the step deviation method, the value of "h" represents\: {
~ The sum of frequencies
= The class interval size
~ The assumed mean
~ The midpoint of a class interval
}

What does "ui" represent in the step deviation method? {
~ (xi + a) / h
= (xi - a) / h
~ fi × xi
~ fi / xi
}

Which of the following is a step in the step deviation method? {
~ Find the midpoints of class intervals
~ Divide di by h
~ Multiply fi by ui
= All of the above
}

If a \= 100, h \= 20, and ui \= 2, what is the step deviation (di)? {
~ 140
= 40
~ 200
~ 20
}

In the step deviation method, which formula is used to calculate the mean (x)? {
= Mean = a + h × (Σ(fi × ui) / Σ(fi))
~ Mean = h × Σ(fi × di)
~ Mean = Σ(fi × xi) / Σ(fi)
~ Mean = Σ(di) / Σ(fi)
}

Why is the assumed mean chosen in the step deviation method? {
= To simplify calculations
~ To eliminate the need for frequencies
~ To reduce class size
~ To calculate di directly
}

If h \= 10, Σ(fi) \= 50, and Σ(fi × ui) \= 100, what is the mean (x), assuming a \= 200? {
~ 210
= 220
~ 300
~ 250
}

What must be true for the step deviation method to be applicable? {
= di values must have a common factor
~ Class intervals must vary in size
~ All fi values must be equal
~ The assumed mean must be 0
}

The step deviation method is derived from\: {
= The direct method
~ The mode formula
~ The median formula
~ The range calculation
}


//True or False

The step deviation method is used to simplify calculations when di values are large. {T}

The assumed mean must always be the smallest xi value in the table. {F}

The formula for mean (x) using the step deviation method includes the class size (h). {T}

The step deviation method eliminates the need to calculate midpoints. {F}

The value of "ui" is calculated by dividing di by h. {T}

//Numericals

If a \= 200, h \= 10, Σ(fi) \= 40, and Σ(fi × ui) \= 80, what is the mean (x)? {
= 220
~ 210
~ 200
~ 230
}

Calculate ui if xi \= 250, a \= 200, and h \= 25. {
~ 2
= 1
~ 4
~ 3
}

If fi \= 5, ui \= 3, and there are 4 intervals, find Σ(fi × ui). {
~ 20
~ 40
= 60
~ 15
}

For mean (x) \= 180, a \= 150, h \= 10, and Σ(fi) \= 30, find Σ(fi × ui). {
= 90
~ 100
~ 30
~ 6
}

//Fill in the blanks

The step deviation method is used to simplify the calculation of the ______. {
~ Median
= Mean (x)
~ Mode
~ Range
}

To calculate "ui," (xi - a) is divided by ______. {
~ fi
~ di
= h
~ Σ(fi)
}

In the formula for mean (x), Σ(fi × ui) is divided by Σ(fi) and multiplied by ______. {
= h
~ a
~ xi
~ di
}

The assumed mean is selected from the values of ______. {
= Class midpoints (xi)
~ Frequencies (fi)
~ Class interval size (h)
~ Deviations (di)
}

The step deviation method is applicable only when there is a common factor in all ______. {
~ Frequencies (fi)
~ Class midpoints (xi)
= Deviations (di)
~ Class intervals
}

In the step deviation method, the class interval size is represented by ______. {
~ Assumed mean (a)
= h
~ ui
~ Σ(fi)
}

The product of fi and ui is calculated in the step deviation method to find the ______. {
~ Median
~ Total frequency
~ Sum of deviations
= Mean (x)
}

The value of "ui" is obtained by dividing ______ by h. {
~ xi
~ a
= di
~ fi
}

The formula for mean (x) in the step deviation method is\: {
= Mean (x) \= a + h × (Σ(fi × ui) / Σ(fi))
~ Mean (x) \= Σ(fi × xi) / Σ(fi)
~ Mean (x) \= a + Σ(fi) / h
~ Mean (x) \= h × Σ(fi × ui)
}

The class interval size (h) is calculated by finding the difference between ______. {
~ Consecutive fi values
= Consecutive class limits
~ Assumed mean and xi
~ Σ(fi) and Σ(fi × ui)
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Mean (x) formula -> Used to calculate the mean
=Class size (h) -> Difference between class limits
=Assumed mean (a) -> Value chosen from xi values
=Step deviation (ui) -> Divides di by h
=Frequency (fi) -> Represents the number of items
}



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