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

//Multiple Choice

What does the term "median" signify in a data set? {
~The most frequent observation
=The value that divides the data into two equal parts
~The average of all observations
~The difference between the highest and lowest values
}

What is the median of the data set\: 5, 12, 8, 20, 15? {
~8
=12
~15
~20
}

If the total number of observations n is odd, the formula for finding the median is\: {
~n/2
=(n+1)/2
~2n+1
~n-1/2
}

In a grouped data, the median class is identified as the class where\: {
~The mean lies
=The cumulative frequency exceeds n/2
~The highest frequency occurs
~The data is evenly distributed
}

If the cumulative frequency before the median class is 40, and n/2 is 50, what is the frequency of the median class? {
~40
~50
=10
~Cannot be determined
}

For ungrouped data, what is the first step to calculate the median? {
~Create a cumulative frequency table
=Arrange data in ascending or descending order
~Find the mean of the data
~Identify the highest and lowest values
}

What is the lower boundary of the class interval 30–40? {
=30
~35
~40
~25
}

Which of the following is NOT required to find the median in grouped data? {
~Lower limit of the median class
~Class size
=Mode of the data
~Cumulative frequency before the median class
}

If the median of a data set is 25 and 50% of observations are below it, what is true about the other 50%? {
=They are greater than or equal to 25
~They are less than 25
~They are equal to 25
~None of the above
}

What type of cumulative frequency distribution is used to find the median in grouped data? {
~More than type
=Less than type
~Both a and b
~None of the above
}

//True or False

The median class is the class interval with the highest frequency. {F}

The cumulative frequency is essential for finding the median in grouped data. {T}

If the total number of observations n is odd, the median is the (n+1)/2th observation. {T}

For ungrouped data, it is not necessary to arrange the data in any order to find the median. {F}

The value of the median separates the data into two equal parts. {T}

//Numericals

Find the median of the data set\: 10, 15, 20, 25, 30, 35, 40. {
~20
=25
~30
~35
}

In a frequency table, the cumulative frequency before the median class is 40, the frequency of the median class is 20, the class width is 10, and the lower limit is 30. Find the median if n\=100. {
~35
=36.67
~40
~45
}

If the class intervals are 0–10, 10–20, 20–30, 30–40, and the respective frequencies are 5, 15, 25, 5, find the median class. {
~0–10
~10–20
=20–30
~30–40
}

//Fill in the blanks

The ________ divides the data into two equal halves. {
=Median
~Mode
~Mean
~Range
}

In ungrouped data, the median is calculated by arranging the observations in ________ order. {
=Ascending
~Descending
~Random
~Any
}

For grouped data, the formula for the median is L + (n/2 - CF)/f * h, where CF is the ________ of the class before the median class. {
=Cumulative frequency
~Total frequency
~Frequency
~Class width
}

If n is odd, the position of the median is given by ________. {
~n/2
=(n+1)/2
~2n+1
~n-1
}

The median class is the class where the ________ lies. {
~Mean
=Cumulative frequency exceeds n/2
~Middle observation
~Range
}

If the cumulative frequency of the class before the median class is 35, and n/2 is 50, the difference is ________. {
=15
~35
~50
~85
}

The lower limit of a class is the ________ value of the class interval. {
~Highest
~Middle
=Smallest
~Average
}

The cumulative frequency of the last class equals the ________ of observations. {
=Total number
~Median
~Mean
~Mode
}

To calculate the median, the class size is represented by the symbol ________. {
=h
~f
~CF
~L
}

The value of the median divides the area under the frequency curve into ________ equal parts. {
=Two
~Three
~Four
~None
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=The role of cumulative frequency in finding the median -> Determines the position of the middle observation
=The significance of the lower boundary in the median formula -> Marks the start of the median class
=The meaning of a "median class" -> Contains the middle observation
=The effect of increasing the class size on the median value -> May slightly shift the median
=The type of data requiring cumulative frequency distribution -> Grouped data
}



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