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

//Multiple Choice

The method of finding the mean by summing all observations and dividing by the number of observations is called the\: {
~ Step Deviation Method
= Direct Method
~ Assumed Mean Method
~ Frequency Distribution Method
}

What is the representative value of a class interval called in grouped data? {
~ Class Width
= Class Mark
~ Frequency
~ Assumed Mean
}

The summation symbol (Σ) is used to indicate\: {
~ Subtraction
= Total Sum
~ Maximum Value
~ Division
}

In the step deviation method, what is "ui" calculated as? {
~ (xi - a)
= (xi - a) / h
~ fi * xi
~ (fi * ui) / h
}

What is the formula for mean in the direct method for grouped data? {
= (Σ fi * xi) / (Σ fi)
~ (Σ fi * ui) / h
~ (Σ xi) / n
~ (Σ di) / (Σ fi)
}

The grouped frequency distribution table is created when\: {
~ Data is small and easy to handle.
= Data is very large and needs classification.
~ Mean is not required.
~ Only ungrouped data is given.
}

What is the class width of the interval 15–20? {
~ 15
= 5
~ 20
~ 10
}

If the sum of frequencies (Σ fi) is 50 and the mean is 25, the total sum of fi * xi is\: {
= 1250
~ 1150
~ 1260
~ 2150
}

The midpoint of the class interval 20–30 is\: {
~ 10
= 25
~ 15
~ 30
}

What is the key advantage of converting ungrouped data into grouped data? {
~ It increases the data size.
= It makes the data easier to interpret.
~ It ensures accuracy in calculations.
~ It eliminates the need for a mean calculation.
}

//True or False

In the direct method, the class mark is the average of the class interval’s upper and lower limits. {T}

The summation symbol (Σ) represents the product of two numbers. {F}

Class intervals in grouped data must always have the same width. {F}

The step deviation method can only be used when all the differences are divisible by a common factor. {T}

The mean obtained from grouped data is always exact. {F}

Converting ungrouped data into grouped data makes calculations easier. {T}

In the direct method, the total of fi * xi is divided by the number of observations. {T}

The class interval 20–30 includes 30 in its frequency count. {F}

The assumed mean is used in both the direct method and the step deviation method. {F}

The frequency of a class interval represents the number of observations in that range. {T}

//Numericals

A grouped frequency table has Σ fi \= 50 and Σ fi * xi \= 1565. Find the mean. 
{ 
    ~ 30.3 
    = 31.3 
    ~ 32.3 
    ~ 33.3 
}

In the step deviation method, if a \= 30, h \= 5, and ui \= (xi - a)/h, calculate ui for xi \= 40. 
{ 
    ~ 1 
    = 2 
    ~ 3 
    ~ 4 
}

//Fill in the blanks

The formula for finding the mean in the direct method for grouped data is _______. {
= Σ (fi * xi) / Σ fi
~ Σ (xi * ui) / Σ fi
~ Σ fi / xi
~ Σ fi * Σ xi
}

_______ is used as a representative of the class interval in grouped data. {
~ Class Width
= Class Mark
~ Assumed Mean
~ Frequency
}

When converting ungrouped data to grouped data, the _______ is used to define intervals. {
~ Class Mark
~ Assumed Mean
= Class Width
~ Summation Symbol
}

In the step deviation method, the assumed mean is denoted by _______. {
= a
~ h
~ ui
~ d. Σ
}

The summation of fi * xi is divided by the summation of _______ to find the mean in the direct method. {
= fi
~ xi
~ h
~ ui
}

The term _______ is used to represent the total frequency in a grouped frequency table. {
~ Class Width
~ Assumed Mean
= Σ fi
~ xi
}

The step deviation method is particularly useful when the values of _______ are large. {
= xi
~ ui
~ fi
~ h
}

In a class interval, the difference between the upper and lower limits is called the _______. {
= Class Width
~ Class Mark
~ Midpoint
~ Frequency
}

The midpoint of the interval 25–35 is _______. {
= 30
~ 25
~ 35
~ 20
}

The method of finding the mean by reducing errors using smaller values is known as _______. {
~ Assumed Mean Method
= Step Deviation Method
~ Direct Method
~ Frequency Distribution Method
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Direct Method -> Σ (fi * xi) / Σ fi
=Step Deviation Method -> Simplifies calculations when data is large
=Class Mark -> Represents the class interval
=Grouped Frequency Table -> Organizes large datasets
=Σ fi -> Total frequency
}



//******** END **********