# mathemerize

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

Question : 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 Solution : We prepare the following table to compute the median : Weight in (kg) Number of students (frequency) …

## 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 surname was obtained as follows :

Question : 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 …

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

Question : 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 Solution : First, we prepare the following table to compute the median : Life time (in hours) Number …

## The lengths of 40 leaves of an plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves.

Question : Length (in mm) 118 – 126 127 – 135 136 – 144 145 – 153 154 – 162 163 – 171 172 – 180 Number of Leaves 3 5 9 12 5 4 2 Solution : Here the frequency table is given in the inclusive form. So, we first convert it into exclusive …

## 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 years.

Question : Age (in years) Number of Policy Holders 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 Solution : We are given the cumulative frequency distribution. So, we first construct a frequency table from the given …

## If the median of the distribution given below is 28.5, find the value of x and y.

Question : Class Interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Total Frequency 5 x 20 15 y 5 60 Solution : Here, it is given that median is 28.5 and n = 60 We now prepare the following cumulative frequency table : Class …

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

Question : Monthly Consumption 65 – 85 85 – 105 105 – 125 125 – 145 145 – 165 165 – 185 185 – 205 Number of Consumers 4 5 13 20 14 8 4 Solution : Monthly Consumption of Electricity No. of Consumers Less than type cumulative frequency 65 – 85 4 4 85 …

## A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data :

Question : Number of cars 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 Frequency 7 14 13 12 20 11 15 8 Solution : The class (40 – 50) has the maximum frequency frequency. Therefore, this is the modal …

## The given distribution shows the number of runs scored by some batsmen of the world in one-day international cricket matches. Find the mode of the data.

Question : Runs scored Number of batsmen 3000 – 4000 4 4000 – 5000 18 5000 – 6000 9 6000 – 7000 7 7000 – 8000 6 8000 – 9000 3 9000 – 10000 1 10000 – 11000 1 Solution : The class (4000 – 5000) has the maximum frequency. Therefore, this is the modal …

## The following distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Question : Number of students per teacher Number of states/U.T. 15 – 20 3 20 – 25 8 25 – 30 9 30 – 35 10 35 – 40 3 40 – 45 0 45 – 50 0 50 – 55 2 Solution : The class (30 – 35) has the maximum frequency. Therefore, this …