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1.  The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Daily Income (Upper Class Limit) Cumulative Frequency Less than 120 12 Less than 140 26 Less than 160 34 Less than 180 40 Less than 200 50 Now, Taking upper class interval on x-axis and their respective frequencies on y-axis,    

7.   The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

   3.7

Class Number of students  Cumulative Frequency 40-45 2 2 45-50 3 5 50-55 8 13 55-60 6 19 60-65 6 25 65-70 3 28 70-75 2 30 MEDIAN:  Median class = 55-60; Lower limit, l = 55;  Cumulative frequency of preceding class, c.f. = 13; f = 6; h = 5 Thus, median weight of the student is 56.67 kg

6.   100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

    3.6

Determine the median number of letters in the surnames. Find the mean number of
letters in the surnames? Also, find the modal size of the surnames.

Class Number of surnames  Cumulative Frequency Class mark 1-4 6 6 2.5 15 4-7 30 36 5.5 165 7-10 40 76 8.5 340 10-13 16 92 11.5 184 13-16 4 96 14.5 51 16-19 4 100 17.5 70     = 100   = 825 MEDIAN:  Median class = 7-10; Lower limit, l = 7;  Cumulative frequency of preceding class, c.f. = 36; f = 40; h = 3 Thus, the median of the data is 8.05 MODE: The...

5. The following table gives the distribution of the life time of 400 neon lamps :
3.5
Find the median life time of a lamp.

Class Frequency   Cumulative Frequency 1500-2000 14 14 2000-2500 56 70 2500-3000 60 130 3000-3500 86 216 3500-4000 74 290 4000-4500 62 352 4500-5000 48 400 Therefore, Median class = 3000-3500 Lower limit, l = 3000; Class height, h = 500 Frequency corresponding to median class, f = 86 Cumulative frequency of the class preceding the median class, c.f. =...

4. The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :

 3.4

Find the median length of the leaves.
(Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to
117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. Class Frequency   Cumulative Frequency 117.5-126.5 3 3 126.5-135.5 5 8 135.5-144.5 9 17 144.5-153.5 12 29 153.5-162.5 5 34 162.5-171.5 4 38 171.5-180.5 2 40 Therefore, Median class = 144.5-153.5 Lower limit, l = 144.5; Class height, h =...

3.  A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.

3.3

Class Frequency   Cumulative Frequency 15-20 2 2 20-25 4 6 25-30 18 24 30-35 21 45 35-40 33 78 40-45 11 89 45-50 3 92 50-55 6 98 55-60 2 100 Therefore, Median class = 35-45 Frequency corresponding to median class, f = 21 Cumulative frequency of the class preceding the median class, c.f. = 24 Lower limit, l = 35; Class height, h = 10 Thus, median age is 35.75 years.

2. If the median of the distribution given below is 28.5, find the values of x and y.

     3.2

Class Number of consumers  Cumulative Frequency 0-10 5 5 10-20 x 5+x 20-30 20 25+x 30-40 15 40+x 40-50 y 40+x+y 50-60 5 45+x+y   = 60   Now, Given median = 28.5 which lies in the class 20-30 Therefore, Median class = 20-30 Frequency corresponding to median class, f = 20 Cumulative frequency of the class preceding the median class, c.f. = 5 + x Lower limit, l...

1.  The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

        3.1

Let the assumed mean be a = 130 and h = 20 Class Number of consumers  Cumulative Frequency Class mark 65-85 4 4 70 -60 -3 -12 85-105 5 9 90 -40 -2 -10 105-125 13 22 110 -20 -1 -13 125-145 20 42 130 0 0 0 145-165 14 56 150 20 1 14 165-185 8 64 170 40 2 16 185-205 4 68 190 60 3 12     = 68       = 7 MEDIAN:  Median class = 125-145; Cumulative Frequency...
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