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Question

In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows: Determine the number of median letters in the surnames. Find the number of mean letters in the surnames and also, find the size of modal in the surnames.

Number of letters

1-4

4-7

7-10

10-13

13-16

16-19

Numbers of surnames

6

30

40

16

4

4


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Solution

Step 1: Compute the median.

Class interval

Frequency

Cumulative Frequency

1-4

6

6

4-7

30

36

7-10

40

76

10-13

16

92

13-16

4

96

16-19

4

100

Given: n=100 and n2=50

Median class=7-10

Therefore, l=7,Cf=36,f=40 and h=3.

Median is given by :

Median=l+n2-Cff×h

⇒Median=7+(50-36)40×3

⇒Median=7+4240

⇒Median=8.05

Step 2: Compute the mode.

Mode is given by:

mode=l+f1-f02f1-f0-f2×h

⇒mode=7+40-30(2×40)-30-16×3

⇒mode=7+3034

⇒mode=7.88

Step 3: Compute the mean.

Class interval

fi

xi

fixi

1-4

6

2.5

15

4-7

30

5.5

165

7-10

40

8.5

340

10-13

16

11.5

184

13-16

4

14.5

51

16-19

4

17.5

70

Sum fi=100

Sum fixi=825

The mean is given by:

mean=∑fixi∑fi

⇒mean=825100

⇒mean=8.25

Hence, the number of median letters in the surnames is 8.05, size of modal in the surnames is 7.88 , and the number of mean letters in the surnames is 8.25.


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