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Solution - Median of Grouped Data

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Question

Below is the given frequency distribution of words in an essay

Number of WordsNumber of Candidates
600 – 8008
800 – 100022
1000 – 120040
1200 – 140018
1400 - 160012

Find the mean number of words written.

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The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day : 

Age (in years)No. of Patients
10-2060
20-3042
30-4055
40-5070
50-6053
60-7020

Find the median age of the patients.

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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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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 Number of surnames
1 - 4 6
4 − 7 30
7 - 10 40
10 - 13 6
13 - 16 4
16 − 19 4

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

Length (in mm)

Number or leaves fi

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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Find the following table gives the distribution of the life time of 400 neon lamps

Life time (in hours) Number of lamps
1500 − 2000 14
2000 − 2500 56
2500 − 3000 60
3000 − 3500 86
3500 − 4000 74
4000 − 4500 62
4500 − 5000 48

Find the median life time of a lamp.

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