calculate the mean, median, mode
TRANSCRIPT
Calculate the Mean, Median, Mode
Presented By
Munna Sir
B.Ed Depart.
Jamshedpur Cooperative College
Question: Calculate the value of Mean(M) for the following data.
CLASS INTERVAL FREQUANCY(f)
0-10 2
10-20 18
20-30 30
30-40 40
40-50 35
50-60 20
60-70 6
70-80 3
Steps for solution
For Mean
1. Calculate the mid point. (mid point = πππππ πππππ+πππππ πππππ
π)
For Example, Mid Point (X) of C.I (0 β 10) = π+ππ
π=
ππ
π= 5
2. Calculate the value of fx. where fx= frequency x mid point.
3. Use formula Mean (M)= βππ
π΅.
CLASS INTERVAL MID POINT(x) FREQUANCY(f)
0-10 5 2
10-20 15 18
20-30 25 30
30-40 35 40
40-50 45 35
50-60 55 20
60-70 65 6
70-80 75 3
βX= 320 βf= 154
CLASS
INTERVAL
MID
POINT(x)
FREQUANCY
(f)fx
0-10 5 2 10
10-20 15 18 270
20-30 25 30 750
30-40 35 40 1400
40-50 45 35 1575
50-60 55 20 1100
60-70 65 6 390
70-80 75 3 225
βX= 320 N = 154 βfx= 5720
Using formula
Mean (M) = βππ
π΅
= ππππ
πππ
= 37.15 Ans.
Question: Calculate the value of Median(Md) for the following data.
CLASS INTERVAL FREQUANCY(f)
90-99 2
80-89 1
70-79 0
60-69 0
50-59 2
40-49 0
30-39 0
20-29 3
10-19 2
SPECIAL CASE: When there are gaps in distribution and N/2 lies more than one C.I.
For Median
1. Change the class interval (If limit are not equal)
2. Calculate the total frequency i.e N.
3. Calculate the value of N/2. And identify two Median group
Md1 & Md2 (upward from N/2 and downward from N/2)
4. Use formula: Median (Md) = π΄π π+π΄π π
π
CLASS
INTERVAL
NEW
CLASS
INTERVAL
FREQUANCY(f) Cumulative
Frequency
(Cf)
90-99 89.5-99.5 2 10
80-89 79.5-89.5 1 8
70-79 69.5-79.5 0 7
60-69 59.5-69.5 0 7
50-59 49.5-59.5 2 7
40-49 39.5-49.5 0 5
30-39 29.5-39.5 0 5
20-29 19.5-29.5 3 5
10-19 9.5-19.5 2 2
N = 10 βcf= 150
βMedian Group 1
π΅
π=
ππ
π= π
βMedian Group 2
Using formula
=ππ.π+ππ.π
π=ππ.π
π= 39.5 Ans
Where, Md1- Upper limit of median group 1(50-59)
i.e 59.5
Md2 β Lower limit of median group 2 (20-29)
i.e 19.5
Md = π΄π π+π΄π π
π
Question: Calculate the value of Mode(Mo) for the following data.
CLASS INTERVAL FREQUANCY(f)
45-49 2
40-44 3
35-39 7
30-34 13
25-29 8
20-24 4
15-19 3
CLASS
INTERVAL
NEW
CLASS
INTERVAL
FREQUANCY(f)
45-49 44.5-49.5 2
40-44 39.5-44.5 3
35-39 34.5-39.5 7 (fa)
30-34 29.5-34.5 13
25-29 24.5-29.5 8 (fb)
20-24 19.5-24.5 4
15-19 14.5-19.5 3
N = 40
βModal Group
Modal Group β highest frequency of C.I.
For Mode
1. Use formula, Mode = L+
Mode = 29.5+
= 29.5+ 2.3
ππ
ππ + ππβ πͺ. π°.
π
π + πβ π
= 31.8 Ans
= 29.5+π
ππβ π
For Query, contact- 8210255915