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 = 𝒍𝒐𝒘𝒆𝒓 𝒍𝒊𝒎𝒊𝒕+𝒖𝒑𝒑𝒆𝒓 𝒍𝒊𝒎𝒊𝒕

𝟐)

For Example, Mid Point (X) of C.I (0 – 10) = 𝟎+𝟏𝟎

𝟐=

𝟏𝟎

𝟐= 5

2. Calculate the value of fx. where fx= frequency x mid point.

3. Use formula Mean (M)= ∑𝒇𝒙

𝑵.

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

∑X= 320 ∑f= 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

∑X= 320 N = 154 ∑fx= 5720

Using formula

Mean (M) = ∑𝒇𝒙

𝑵

= 𝟓𝟕𝟐𝟎

𝟏𝟓𝟒

= 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) = 𝑴𝒅𝟏+𝑴𝒅𝟐

𝟐

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 ∑cf= 150

←Median Group 1

𝑵

𝟐=

𝟏𝟎

𝟐= 𝟓

←Median Group 2

Using formula

=𝟏𝟗.𝟓+𝟓𝟗.𝟓

𝟐=𝟕𝟗.𝟎

𝟐= 39.5 Ans

Where, Md1- Upper limit of median group 1(50-59)

i.e 59.5

Md2 – Lower limit of median group 2 (20-29)

i.e 19.5

Md = 𝑴𝒅𝟏+𝑴𝒅𝟐

𝟐

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

←Modal Group

Modal Group – highest frequency of C.I.

For Mode

1. Use formula, Mode = L+

Mode = 29.5+

= 29.5+ 2.3

𝒇𝒂

𝒇𝒂 + 𝒇𝒃∗ 𝑪. 𝑰.

𝟕

𝟕 + 𝟖∗ 𝟓

= 31.8 Ans

= 29.5+𝟕

𝟏𝟓∗ 𝟓

For Query, contact- 8210255915