Estimated Mode equation

The Estimated Mode calculator computes the estimated mode based on the Lower Class boundary of the group containing median, the Number of Observations, the cumulative frequency of groups before median group, the frequency of median group and the group width.

INSTRUCTIONS: Enter the following:

• (L) Lower Boundary of Median Group
• (fm) Frequency in Median Group
• (fmb) Frequency Before Median Group
• (fma) Frequency After Median Group
• (w) Median Group Width 

Estimated Median (Mode_EST): The calculator returns the estimated median.

The Math / Science

The formula for the estimated mode of a group is:

          `Mode_(EST)=  L+ ((fm-fmb)/(fm-fmb+fm-fma))*w`

where:

• Mode_EST = Estimated Mode
• L = Lower Boundary of Median Group
• fm = Frequency in Median Group
• fmb = Frequency Before Median Group
• fma = Frequency After Median Group
• w = Median Group Width

The Estimated Median of a Group is used to calculate estimated median of a group data. For example

The Median is the mean of the ages of the 56^th and the 57^th people, so is in the 20 - 29 group:

• L = 20 (the lower class boundary of the class interval containing the median)
• n = 112
• F = 20 + 21 = 41
• f_m = 23
• w = 10

  `M_"EST"  = 20 + ( (112/2) - 41)/24 * 10`

Estimated Statistics

• Estimated Median
• Estimated Mode
• Estimated Mean
• Standard Deviation of Mean (SDOM)