Averages

Omtex – classes “THE HOME OF TEXT”

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Average: An average is a single value which is used to describe the entire mass of data. For e.g. A boy got 60 % in S.S.C • Types of averages: 1. Arithmetic mean (A.M) 2. Median (C.F) 3. Mode 1. Arithmetic mean: • Simple A.M X = ∑ X X= 1,2,3,4,………………n n

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Arithmetic mean for GROUPED DATA X 10 12 13

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f 2 3 1

fx 20 24 13

Arithmetic mean with C.I

C.I 0-10 10-20 20-30

X = ∑fx ∑f

X

F 2 3 4

X 5 15 25

= ∑fx ∑f

fx 10 45 100

2. Median: Median is the value of middle observation when data is arranged in

ascending order of their magnitude. • Simple median: If there are an even numbers of observation then median is average of two middle observations. E.g. 3, 8, 12, 6, 9, 4. Arranging in ascending order 3, 4, 6, 8, 9, 12 Median = M = 6 + 8 = 14 = 7 2 2 If there are an odd numbers of observations then median is the value of middle observation E.g. 2,7,5,4,1 Arranging in ascending order 1,2,4,5,7 Median = M = 4 •

Median for grouped data: X

F

c.f

1

Omtex – classes “THE HOME OF TEXT”

10 11 12 13 N = 10

2 3 4 1

2 5 9 10

N = 10 ∑f + 1 = 10 + 1 = 5.5 2 2 Therefore, Median M = 12 •

Median for Class – interval. (IMP.) C.I 0-10 10-20 20-30 30-40 40-50 Median = M = l1+

f 2 3 4 5 1 ∑f = 15

cf 2 5 9 14 15

(l2 – l1) ( ∑f /2 – cf ) f

Where: N/2 = 15/2 = 7.5 Where: l1 = 20 & l2 = 30 Where: f = 4 & cf = 5 3. Mode: Mode is that value of the observation which appears most frequently (i.e. with greatest frequency) In other words, It is the value around which the items tend to be most heavily concentrated. • Simple mode: Find mode from the following numbers, 1, 2, 180, 5, 63, 24, 2, 14, 2 Here the mode is 2 since 2 have repeated maximum times. When there are two or more values with greatest frequency, mode is said to be ill – defined, such a series is also known as bi-modal or multi-modal. E.g. 23, 25, 27, 23, 32, 25, 64, 27 Here the mode is 23, 25 & 27 since these three numbers repeated more but same as 2 times.

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Omtex – classes “THE HOME OF TEXT”

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Mode for grouped data: X 10 11 12 13

F 2 3 4 1

Here Mode = 12 since it has maximum frequency of 4.

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Mode for class – interval C.I 0-10 10-20 20-30 30-40 40-50 Here Mode = l1 +

f 2 3 4 5 1 ∑f = 15 (l2 – l1)(f1 – f0) (2f1-f0-f2)

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