In mathematics frequency distribution is used in statistics. Mean of a frequency distribution is that the arrangement in which sets of value occurs and in the values one or more variable takes place. Frequency distribution is in the form of either graphical or tabular. Each value in the table contains frequency or count of values, how many times they occur. The values of frequency in group or interval forms. After summarizing the entire values frequency distribution table is formed. Mean of frequency distribution is also that it shows the total number of observations within a given interval. The interval is either exclusive or exhaustive. The size of intervals generally depends on the data which we have to analyze and calculate. One thing we have to remind that the intervals must not be overlapped to each other.
Now we discuss that how to construct frequency distribution tables. We use some steps to make a frequency distribution table. In step one; we determine the range of given data. Range of given data means the difference between the higher value and the lower value. In step two, we decide that which data can be grouped means formulation of approximate number of groups. There are no particular rules for step two. It can be 5 groups to 15 groups. But there is one formula for this (K=1+3.322logN), where K is the no of groups, logN is the total number of observations.
In step third, we decide the size of intervals. The size of interval is denoted by (h). To determine the size we can use a formula (h= range/number of groups). If result is in fraction then we choose next higher value. In step fourth, we decide start point means starting from the lowest value and in the ascending order. In step fifth, we determine the remaining groups. It is determined by adding the interval size corresponding to all values. In step sixth, we distribute all the data into their groups. For this we use tally marks method because it is suitable for tabulating the observations into their respective groups. By using these six steps we can construct a frequency distribution table.
Now we come to standard deviation for frequency distribution. It is a measure of variation or measure of dispersion amongst the data. In place of taking absolute deviation we may square each deviation and obtained the variance. The square root value of variance is known as standard deviation for given values of frequency.
Now we discuss that how to construct frequency distribution tables. We use some steps to make a frequency distribution table. In step one; we determine the range of given data. Range of given data means the difference between the higher value and the lower value. In step two, we decide that which data can be grouped means formulation of approximate number of groups. There are no particular rules for step two. It can be 5 groups to 15 groups. But there is one formula for this (K=1+3.322logN), where K is the no of groups, logN is the total number of observations.
In step third, we decide the size of intervals. The size of interval is denoted by (h). To determine the size we can use a formula (h= range/number of groups). If result is in fraction then we choose next higher value. In step fourth, we decide start point means starting from the lowest value and in the ascending order. In step fifth, we determine the remaining groups. It is determined by adding the interval size corresponding to all values. In step sixth, we distribute all the data into their groups. For this we use tally marks method because it is suitable for tabulating the observations into their respective groups. By using these six steps we can construct a frequency distribution table.
Now we come to standard deviation for frequency distribution. It is a measure of variation or measure of dispersion amongst the data. In place of taking absolute deviation we may square each deviation and obtained the variance. The square root value of variance is known as standard deviation for given values of frequency.
