Creating Grouped Frequency Distributions

Creating Grouped Frequency Distribution:

A) At first we have to determine the biggest and smallest values.

B) Then we have to Calculate the Range = Maximum - Minimum

C) Choose the number of classes wished for. This is generally between 5 to 20.

D) Find out the class width by dividing the range by the number of classes and then rounding up. We have to keep in mind that we must round up, not off. Generally 4.2 would round to be 4, however in rounding up, it becomes 5. When the range divided by the number of classes gives an integer value (without any remainder), then you can either add up one to the number of classes or add up one to the class width. Sometimes you are locked to a certain number of classes as of instructions. The Bluman text fails to state the case when there is no remainder.

E) Choose an appropriate starting point less than or equivalent to the minimum value. "The class width times, the number of classes" values ware most capable to cover. We require covering one more value than the range. We can finely follow the rule: The beginning point plus the number of class’s times the class width should be bigger than the maximum value. Here the lower limit is the starting point of the first class. We can get the rest of lower limits by continuously adding the class width to this lower limit.

F) To getting the upper limit of first class, we can subtract one from the lower limit of second class. Then carry on adding the class width to this upper limit to determine the rest of the upper limits.

G) Find out the boundaries by subtracting 0.5 units from lower limits and adding up to 0.5 units from upper limits. The boundaries are as well half-way among the upper limit of one class and the lower limit of subsequent class. It is not essential to find the boundaries whether you are trying to achieve it.

H) Now tally the data.

I) Find out the frequencies.

J) Now determine the cumulative frequencies. Based on what you are trying to achieve, it might not be essential to determine the cumulative frequencies.

K) Whenever essential, find out the relative frequencies and or relative cumulative frequencies.

To find the frequencies, it is possible to have TI-82 calculator for you. Initially we will have to determine the class width and class boundaries.

Lists and Statistics:

Lists and Statistics are the two features which TI-82 calculator will be used. The STAT key is positioned at the top center of the calculator and the LIST key is received by second STAT.

There is a list of six which you can work with at any time on calculator. Each and every set of data needs a list. Whenever you comprise frequencies for the frequency distribution, then it will need a list for the data and split the list for frequencies. L1, L2, L3, L4, L5 and L6 are labeled and are accessed on the calculator by pressing the "2nd 1", "2nd 2", and so on.


EDIT and CALC are the two major categories of STATS.


A) Edit: We can use this to enter the data to the list.

B) SortA(: It will sort the list in ascending order. If you want to find the frequencies, this is very useful after you have previously established the limits or boundaries. As the data is sorted in an order, you simply have to go through and count the number in each and every class. You do not require doing the tally. This will change the list you state it sort.

C) SortD(: It will sort the list in descending order. This will substitute the list you state it to sort.

D) ClrList: The existing lists are erased by using ClrList.


A) 1-Var Stats: When there is only one variable then this is mainly used. This will handle both frequency and raw data distributions.

B) 2-Var Stats: When there are two variables x and y then this is used. This won't occur until the end of semester.

C) Setup: We have to check the setup initially before we find any other statistical values from the menu. It permits you to specify which lists you place the data into and if essential, that list comprise the frequencies.

D) Med-Med: It is a regression model which is not used in this topic.

E) LinReg(ax+b): After talking about two variable statistics, this regression model will be used later.

F) QuadReg: It is a regression model which is not used in this topic.

G) CubicReg: It is a regression model which is not used in this topic.

H) QuartReg: It is a regression model which is not used in this topic.

I) LinReg(ax+b): After talking about two variable statistics, this regression model will be used later.

J) LnReg: It is a regression model which is not used in this topic.

K) ExpReg: It is a regression model which is not used in this topic.

L) PwrReg: It is a regression model which is not used in this topic.


OPS (Operations) and MATH are the two major sections of the LIST command.


A) SortA(: In this, the sorting can be done in ascending order. Under the STATS key this command is equivalent to SortA(command.

B) SortD(: In this, the sorting can be done in descending order. Under the STATS key this command is equivalent to SortD(command.

C) dim: The dimension of list is returned by this function. The dimension of the list is the number of elements in list. This is as well used as a command to set the dimensions of a list.

D) Fill(: The list is filled with a constant by using this command. This is very useful when you require setting a whole list to all be one number.

E) seq: According to the function specified as the first argument this function will produce a series of numbers. The list is returned, however you should save it to one of the six lists whenever you want to employ it for anything.


A) min(: It returns the minimum value in list.

B) max(: It returns the maximum value in list.

C) mean(: It returns the arithmetic mean of all the numbers in list. The mean is the addition of the list divided by the dimension of list.

d) median(: It returns the median of list. When the list is sorted in ascending order then median is the middle number. Whenever the dimension is an even number, then median is the mid-point between the two middle values if the list is sorted in ascending order.

e) sum: It returns the sum of values in a list.

f) prod: Returns the product of the values in list. If the product of a list is zero, then at-least one of the numbers is 0 (zero).

Other Keys

VARS: To retrieve the value of statistic the VARS key can be employed.

VARS Statistics

It will save a lot of re-typing of values and permit you to fully use the accuracy of calculator rather than losing digits whenever re-entering the numbers.

Some of the common values that will be used are given below:

Keystrokes     Statistic
VARS 5 1     n, the sample size
VARS 5 1     x bar, the sample mean
VARS 5 1     Sx, the sample standard deviation
VARS 5 1     minX, the minimum value
VARS 5 1     maxX, the maximum value

There are some other values beneath statistics which we will utilize. You might have to arrow to other sub menus first for some of them.


The values are saved by this key. You might save a scalar value to the real variable (A to Z) or a list value to a list (L1 to L6). You can employ the STORE key to save value to the dimension of list to set its size. The STORE key can be use to save a list generated by the sequence command to list.

Mathematical Operations and Functions:

The lists can be employed as arguments of functions. Whenever they are, the function is applied to each and every element in the list. Mathematical operations can be executed on lists.

Entering Data:

Always begin with a clean set of data. You do not want to mix data from one problem with the data from the other problem. Before beginning any new problem, you must clear out present data.

STAT ClrList L1,L2,L3

The other way to clear the lists is to go to STAT EDIT, arrow to the top and hence the list name is highlighted. Now press the CLEAR key and ENTER.

You may only require specifying one list, but you can specify more than one, just separate them with commas.

When the lists have been cleared, you can enter the latest lists:

STAT Edit:

Choose this list that you want to utilize. The default will be L1. This will be excellent for most things; however do realize you can employ any of the lists. Now be sure to confirm the setup later.

Type in each number sorting out them by enters. Whenever you are completed entering, press the QUIT key (that is, 2nd MODE). Whenever you need to correct the data, just go back to STAT EDIT devoid of clearing the list first.

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