Calculating the Median from Grouped Data

Statisticians use the following equation to determine the median of groped data:

                              l = Lower limit of the median class,
                              h = width of the median class,
                              f = frequency of the median class
                              c = cumulative frequency of the class preceding the
                                    median class
                              n = total frequency
Problem: Calculate the median days of maturity of 40-short term investments.
 Table: 8

Class interval	Frequency (fi)	Cumulative frequency
30—39	3	3
40—49	1	4
50—59	8	12
60—69	10	22
70—79	7	29
80—89	7	36
90—99	4	40
Total	40

If we use the above equation to compute the median of data of days to maturity 40 short-term investments in Table 8, then n/2 = 20, median class is  60-69, l = 60, h = 10, f = 10, c = 12. Then

Mode: The mode, if one exists, is the most frequently occurring value.

Example: The demand for bottled water increases during the hurricane season in Florida. A random sample of 7 hours showed that the following numbers of 1-gallon bottles were sold in one store:
        
                     40     43     62     43     50     60     65
The mode is 43 bottles, since it occurs twice and all the other number of bottles occur only once. However, the mode in this case is the smallest value and is not the best indicator of central tendency. If the sample included a eighth hour number of bottles of 65:  

                      40     43     43     50     60     62     65   65
we see that the data are bimodal, which modes are 43 and 65.