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Standard X

Mathematics

Empirical Relationship of the three measures of central tendency

Show that the...

Question

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

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Solution

Mode of $S_{1}$ = 9
Mode of $S_{2}$ = 7

After combining $S_{1}$ and $S_{2}$ , the new series is 3, 5, 8, 8, 9, 12, 13, 9, 9, 7, 4, 7, 8, 7, 8, 13.

Mode of combined series = 8

Mode of $S_{1}, S_{2}$ is different from mode of $S_{1}$ and mode of $S_{2}$ separately.

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Show that the mode of the series obtained by combining the two series S1 and S2 given below is different from that of S1 and S2 taken separately: S1 : 3, 5, 8, 8, 9, 12, 13, 9, 9 S2 : 7, 4, 7, 8, 7, 8, 13

Mode of S1 = 9 Mode of S2 = 7 After combining S1 and S2, the new series is 3, 5, 8, 8, 9, 12, 13, 9, 9, 7, 4, 7, 8, 7, 8, 13. Mode of combined series = 8 Mode of S1,S2 is different from mode of S1 and mode of S2 separately.

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

Mode of $S_{1}$ = 9
Mode of $S_{2}$ = 7

After combining $S_{1}$ and $S_{2}$ , the new series is 3, 5, 8, 8, 9, 12, 13, 9, 9, 7, 4, 7, 8, 7, 8, 13.

Mode of combined series = 8

Mode of $S_{1}, S_{2}$ is different from mode of $S_{1}$ and mode of $S_{2}$ separately.