question_answer

Show that the mode of the series obtained by combining the two series \[{{S}_{1}}\] and \[{{S}_{2}}\] given below is different from that of \[{{S}_{1}}\] and \[{{S}_{2}}\] taken separately:

\[{{S}_{1}}:3,\,\,5,\,\,8,\,\,8,\,\,9,\,\,12,\,\,13,\,\,9,\,\,9\]

\[{{S}_{2}}:7,\,\,4,\,\,7,\,\,8,\,\,7,\,\,8,\,\,13\]

Answer:

Mode of \[{{S}_{1}}\] series \[=9\]

Mode of \[{{S}_{2}}\] series \[=7\]

After combining \[{{S}_{1}}\] and \[{{S}_{2}}\], the new series will be = 3, 5, 8, 8, 9, 12, 13, 9, 9, 7, 4, 7, 8, 7, 8, 13.

Mode of combined series = 8 (maximum times)

Mode of \[({{S}_{1}},{{S}_{2}})\] is different from mode of \[{{S}_{1}}\] and mode of \[{{S}_{2}}\] separately.          Hence Proved.