How to get xlb in statistics?

Quartiles are values that split up a dataset into four equal parts.

You can use the following formula to calculate quartiles for grouped data:

Qi = L + (C/F) * (iN/4 – M)

where:

The following example shows how to use this formula in practice.

Suppose we have the following frequency distribution:

Now suppose we’d like to calculate the value at the third quartile (Q3) of this distribution.

The value at the third quartile will be located at position (iN/4) in the distribution.

Thus, (iN/4) = (3*92/4) = 69.

The interval that contains the third quartile will be the 21-25 interval since 69 is between the cumulative frequencies of 58 and 70.

Knowing this, we can find each of the values necessary to plug into our formula:

L: The lower bound of the interval that contains the ith quartile

C: The class width

F: The frequency of the interval that contains the ith quartile

N: The total frequency

M: The cumulative frequency leading up to the interval that contains the ith quartile

We can then plug in all of these values into the formula from earlier to find the value at the third quartile:

The value at the third quartile is 24.67.

You can use a similar approach to calculate the values for the first and second quartiles.

1 answer"After some consideration, in my opinion, "lower boundary" will make more sense rather than lower limit. For example, this is the data, Class Frequency 1 1 2 1 3 .

Mean = 74.57 Median = 72.5 Mode = 68.5

Step-by-step explanation:

Mean

In computing the mean for grouped data, use the formula

Mean = fM/n

f=class frequency

M=Midpoint or class mark

N=number of cases

Now let's solve first the midpoint.

Midpoint = (lower limit + upper limit)/2

Class Interval     Frequency      Midpoint        fM (Frequency x Midpoint)

89-99                         5                    94                                470

78-88                         6                     83                               498

67-77                         10                    72                               720

56-66                        9                    61                               549

30                                                       2237

Mean = fM/N

Mean = 2237/30

Mean = 74.57

Median

The formula in solving median of a grouped data is

Median = Xlb + i

X = lower boundary of median class

fm = frequency of the median class

i = class size

Class Interval     Frequency      Cumulative Frequency

89-99                         5                    30      (25+5)

78-88                         6                    25      (19+6)

67-77                         10                    19      (9+10)

56-66                        9                    9

30

To determine the median class, divide N by 2. Thus, 30/2 is equal to 15. Therefore, our median class is the classes with frequency of 10.

Class Interval     Frequency      Cumulative Frequency

89-99                         5                    30      (25+5)

78-88                         6                    25      (19+6)

67-77                         10                    19     (9+10)

56-66                        9                    9

30

Now let's solve for the median.

Median = Xlb + i

Median = 66.5 + 10

Median = 72.5

*lower boundary = lower limit - 0.5

*upper boundary = upper limit + 0.5

Mode

In solving the ode of a grouped data, we are going to use the formula

Mode = X + i

X = Lower boundary of the modal class

A = Difference of Highest frequency and the frequency below it

B =  Difference of Highest frequency and the frequency above it

To determine the modal class, look for the group with the highest frequency.

Class Interval     Frequency

89-99                         5

78-88                         6

67-77                         10

56-66                        9

30

Now let's solve for the mode.

Mode = X + i

Mode = 66.5 + 10

— To calculate the mean of grouped data, the first step is to determine the midpoint (also called a class mark) of each interval, or class. These .

𝑋𝐿𝐵 = the lower boundary or true lower limit of the median class. N = total frequency 𝑐𝑓𝑏 = cumulative frequency before the median class 𝑓𝑚 = frequency ."Rating: 1 · 1 vote