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

//Multiple Choice

What is the primary reason for using the assumed mean method to calculate the mean of grouped data? {
~ To avoid errors
= To simplify calculations
~ To handle ungrouped data
~ To make data continuous
}

In the assumed mean method, what is represented by "di"? {
~ The difference between class intervals
= The difference between an assumed mean and a class mark
~ The product of frequency and class mark
~ The summation of frequencies
}

If the assumed mean a \= 50, and xi \= 60, what is di? {
= 10
~ -10
~ 50
~ 60
}

The formula to calculate the mean using the assumed mean method is\: {
~ Mean \= (Sum of fi * xi) / (Sum of fi)
= Mean \= a + (Sum of fi * di) / (Sum of fi)
~ Mean \= (Sum of di) / (Sum of fi)
~ Mean \= (Sum of xi) / (Sum of fi)
}

In grouped data, the midpoint of a class interval is also known as\: {
~ Class width
= Class mark
~ Frequency
~ Assumed mean
}

What is the midpoint of the class interval 30–40? {
= 35
~ 40
~ 30
~ 70
}

What is the necessary operation to calculate fi * di? {
~ Addition
~ Subtraction
= Multiplication
~ Division
}

What is the first step in the assumed mean method? {
~ Choosing a class mark
~ Calculating deviations
= Selecting an assumed mean
~ Summing the frequencies
}

If the class interval is 10–20 and the class mark is 15, what is the width of the class? {
~ 5
= 10
~ 15
~ 20
}

Why is an assumed mean chosen from xi? {
= To reduce calculations
~ To find the midpoint
~ To calculate frequencies
~ To make the class continuous
}

//True or False

The assumed mean method simplifies the calculation of the mean. {T}

di \= xi + a in the assumed mean method. {F}

The class mark is calculated as the sum of the class limits divided by two. {T}

The assumed mean must be a value within the range of the class marks. {T}

The deviation di is always positive. {F}

To make a class continuous, half the gap between class intervals is added and subtracted appropriately. {T}

The midpoint of the interval 20–30 is 25. {T}

In grouped data, frequencies correspond to individual data points. {F}

fi * di is the product of deviation and frequency in the assumed mean method. {T}

The width of a class interval is the difference between consecutive lower or upper limits. {T}

//Numericals

Calculate the midpoint of the class interval 25–35. {
~ 25
= 30
~ 35
~ 40
}

If a \= 20, xi \= 25, and fi \= 5, what is fi * di? {
= 25
~ -25
~ 5
~ 20
}

For the class intervals 10–20, 20–30, 30–40, what is the class width? {
~ 5
= 10
~ 15
~ 20
}

If the summation of fi is 50, and the summation of (fi * di) \= 100, what is the mean deviation? {
~ 50
= 2
~ 200
~ 20
}

The mean of a data set calculated by the assumed mean method is a \= 10, (Sum of fi * di) / (Sum of fi) \= 2. What is the mean? {
~ 8
~ 10
= 12
~ 20
}

//Fill in the blanks

The assumed mean method simplifies the process of calculating the ______ of grouped data. {
~ Median
= Mean
~ Mode
~ Range
}

In the assumed mean method, di is calculated as the difference between a class mark and the ______. {
~ Frequency
= Assumed mean
~ Class interval
~ Summation
}

To find the mean, the ______ of (fi * di) is divided by the summation of fi. {
~ Product
= Summation
~ Difference
~ Division
}

fi * di represents the ______ of frequency and deviation. {
= Product
~ Sum
~ Difference
~ Ratio
}

The deviation di is multiplied by the corresponding ______ to get fi * di. {
~ Class width
~ Class mark
= Frequency
~ Summation
}

In the assumed mean method, the mean is calculated using "a + (Sum of fi * di) / ______". {
~ Class mark
~ xi
= fi
~ Width
}

If the class interval is 50–60, the class mark is ______. {
~ 50
= 55
~ 60
~ 65
}

In grouped data, xi represents the ______ of the class interval. {
~ Mean
= Midpoint
~ Frequency
~ Deviation
}

The assumed mean is denoted by ______. {
~ di
~ fi
= a
~ xi
}

Half the class gap is added to the upper limit and subtracted from the lower limit to make the class ______. {
= Continuous
~ Midpoint
~ Wider
~ Smaller
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Class mark -> Midpoint of the class interval
=Assumed mean (a) -> A value chosen from the class marks to simplify calculations
=Continuous class intervals -> Class intervals without gaps between consecutive limits
=fi -> Frequency of the class interval
=di -> Deviation between the class mark and assumed mean
}



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