find the mode of data 65-85 85-105 105-125 125-145 145-165 165-185 185-205. frequency is 4,5,13,20,14,8,4?
Answers
Step-by-step explanation:
Interval Frequency Cumulative frequency
65-85 4 4
85-105 5 9
105-125 13 22
125-145 20 42
145-165 14 56
165-185 8 64
185-205 4 68
N = 68
Here; n = 68 and hence
n
2
=
34
So, median class is 125-145 with cumulative frequency = 42
now,
l
=
125
,
n
=
68
,
c
f
=
22
,
f
=
20
,
h
=
20
Median can be calculated as follows:
Median
=
l
+
n
2
−
c
f
f
×
h
=
125
+
34
−
22
20
×
20
=
125
+
12
=
137
Calculations for Mode:
Modal class
=
125
−
145
,
f
1
=
20
,
f
0
=
13
,
f
2
=
14
and
h
=
20
Mode
=
l
+
(
f
1
−
f
0
2
f
1
−
f
0
−
f
2
)
×
h
=
125
+
20
−
13
2
×
20
−
13
−
14
×
20
=
125
+
7
13
×
20
=
125
+
10.77
=
135.77
Calculations for Mean:
Class Interval fi xi di = xi - a ui = di/h fiui
65-85 4 75 -60 -3 -12
85-105 5 95 -40 -2 -10
105-125 13 115 -20 -1 -13
125-145 20 135 0 0 0
145-165 14 155 20 1 14
165-185 8 175 40 2 16
185-205 4 195 60 3 12
Σ fi = 68 Σ fiui = 7
x
=
a
+
Σ
f
i
u
i
Σ
f
i
×
h
=
135
+
7
68
×
20
=
137.05
Mean, median and mode are more or less equal in this distribution.