$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
Number of letters Number of surnames
$1-4$ $6$
$4-6$ $30$
$6-8$ $44$
$8-12$ $16$
$12-20$ $4$

$(i)$ Draw a histogram to depict the given information.
$(ii)$ Write the class interval in which the maximum number of surnames lie.

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(N/A) $(i)$ Here,it can be observed that the data has class intervals of varying width. The proportion of the number of surnames per $2$ letters interval can be calculated as follows:
Number of letters Frequency (Number of surnames) Width of class Length of rectangle
$1-4$ $6$ $3$ $\frac{6 \times 2}{3} = 4$
$4-6$ $30$ $2$ $\frac{30 \times 2}{2} = 30$
$6-8$ $44$ $2$ $\frac{44 \times 2}{2} = 44$
$8-12$ $16$ $4$ $\frac{16 \times 2}{4} = 8$
$12-20$ $4$ $8$ $\frac{4 \times 2}{8} = 1$

By taking the number of letters on the $x$-axis and the proportion of the number of surnames per $2$ letters interval on the $y$-axis,the histogram is constructed as shown in the provided image.
$(ii)$ The class interval in which the maximum number of surnames lies is $6-8$,as it contains $44$ surnames,which is the maximum frequency for this data.

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Similar Questions

$A$ survey conducted by an organisation for the cause of illness and death among women between the ages $15-44$ (in years) worldwide,found the following figures (in $\%$):
$S$.NoCausesFemale fatality rate $(\%)$
$1.$Reproductive health conditions$31.8$
$2.$Neuropsychiatric conditions$25.4$
$3.$Injuries$12.4$
$4.$Cardiovascular conditions$4.3$
$5.$Respiratory conditions$4.1$
$6.$Other causes$22.0$

$(i)$ Represent the information given above graphically.
$(ii)$ Which condition is the major cause of women's ill health and death worldwide?
$(iii)$ Try to find out,with the help of your teacher,any two factors which play a major role in the cause in $(ii)$ above being the major cause.

Classify the data you can collect from your day-to-day life as primary or secondary data.
In our day-to-day life,we can collect the following data:
$1.$ Number of females per $1000$ males in various states of our country.
$2.$ Weights of students of our class.
$3.$ Production of wheat in the last $10$ years in our country.
$4.$ Number of plants in our locality.
$5.$ Rainfall in our city in the last $10$ years.

Consider the marks obtained by $10$ students in a mathematics test as given below:
$55, 36, 95, 73, 60, 42, 25, 78, 75, 62$

The relative humidity (in $\%$) of a certain city for a month of $30$ days was as follows:
$98.1$ $98.6$ $99.2$ $90.3$ $86.5$ $95.3$ $92.9$ $96.3$ $94.2$ $95.1$
$89.2$ $92.3$ $97.1$ $93.5$ $92.7$ $95.1$ $97.2$ $93.3$ $95.2$ $97.3$
$96.2$ $92.1$ $84.9$ $90.2$ $95.7$ $98.3$ $97.3$ $96.1$ $92.1$ $89$

$(i)$ Construct a grouped frequency distribution table with classes $84-86, 86-88$,etc.
$(ii)$ Which month or season do you think this data is about?
$(iii)$ What is the range of this data?

Consider the marks,out of $100$,obtained by $51$ students of a class in a test,given in the table below. Draw a frequency polygon corresponding to this frequency distribution table.
MarksNumber of students
$0-10$$5$
$10-20$$10$
$20-30$$4$
$30-40$$6$
$40-50$$7$
$50-60$$3$
$60-70$$2$
$70-80$$2$
$80-90$$3$
$90-100$$9$
Total$51$

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