76
Question
Calculate mode from following data:
Class Interval5−1415−2425−3435−4444−5455−64Frequency81015254020.
Calculate mode from following data:
Class Interval5−1415−2425−3435−4444−5455−64Frequency81015254020.
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Solution
Lets form the frequency table by converting into continuous class interval for finding mode.
Class Intervalxf5−144.5–14.5815−2414.5–24.51025−3424.5–34.51535−4434.5–44.525 [f0]45−54 [L] 44.5–54.540 [f1]55−6454.5–64.520 [f2]
In frequency, 40 is the highest frequency.⇒ Modal class =44.5–54.5
From the table,
L=44.5 [Lower boundary]
f1=40
f0=25
f2=20
Size of the class interval (h)=10
Mode =L+(f1−f02f1−(f0+f2))h
=44.5+(40−252(40)−(25+20))10
=44.5+(1580−45))10
=44.5+15035
=44.5+4.28 (Approximately)
=48.78 (Approximately)
Thus, the mode of the given data is 48.78.
Lets form the frequency table by converting into continuous class interval for finding mode.
Class Intervalxf5−144.5–14.5815−2414.5–24.51025−3424.5–34.51535−4434.5–44.525 [f0]45−54 [L] 44.5–54.540 [f1]55−6454.5–64.520 [f2]
In frequency, 40 is the highest frequency.
⇒ Modal class =44.5–54.5
From the table,
L=44.5 [Lower boundary]
f1=40
f0=25
f2=20
Size of the class interval (h)=10
Mode =L+(f1−f02f1−(f0+f2))h
=44.5+(40−252(40)−(25+20))10
=44.5+(1580−45))10
=44.5+15035
=44.5+4.28 (Approximately)
=48.78 (Approximately)
Thus, the mode of the given data is 48.78.
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