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.
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