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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: | Number of letters | 1-4 | 4-7 | 7-10 | 10- 13 | 13-16 | 16-19 | | Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |
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.
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The distribution below gives the weights of 30 students of a class. Find the median weight of the students. | Weight(in kg) | 40-45 | 45-50 | 50-55 | 55- 60 | 60-65 | 65-70 | 70-75 | | Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
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The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them. | Monthly consumption(in units) | No. of customers |
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| 65-85 | 4 | | 85-105 | 5 | | 105-125 | 13 | | 125- 145 | 20 | | 145-165 | 14 | | 165-185 | 8 | | 185- 205 | 4 |
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If the median of a distribution given below is 28.5, find the value of x & y. | Class Interval | Frequency |
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| 0- 10 | 5 | | 10-20 | x | | 20-30 | 20 | | 30-40 | 15 | | 40- 50 | y | | 50-60 | 5 | | Total | 60 |
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The life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to the persons whose age is 18 years onwards but less than the 60 years. | Age (in years) | Number of policy holder |
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| Below 20 | 2 | | Below 25 | 6 | | Below 30 | 24 | | Below 35 | 45 | | Below 40 | 78 | | Below 45 | 89 | | Below 50 | 92 | | Below 55 | 98 | | Below 60 | 100 |
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The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table: | Length (in mm) | Number of leaves |
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| 118-126 | 3 | | 127-135 | 5 | | 136-144 | 9 | | 145- 153 | 12 | | 154-162 | 5 | | 163-171 | 4 | | 172- 180 | 2 |
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.)
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The following table gives the distribution of a lifetime of 400 neon lamps. | Lifetime (in hours) | Number of lamps |
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| 1500-2000 | 14 | | 2000-2500 | 56 | | 2500- 3000 | 60 | | 3000-3500 | 86 | | 3500-4000 | 74 | | 4000- 4500 | 62 | | 4500-5000 | 48 |
Find the median lifetime of a lamp.
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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: | Number of letters | 1-4 | 4-7 | 7-10 | 10- 13 | 13-16 | 16-19 | | Number of surnames | 6 | 30 | 40 | 16 | 4 | 4 |
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.
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Answer
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The distribution below gives the weights of 30 students of a class. Find the median weight of the students. | Weight(in kg) | 40-45 | 45-50 | 50-55 | 55- 60 | 60-65 | 65-70 | 70-75 | | Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
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