Exercise 18
Question 1
1. A total of 20 patients admitted to a hospital have blood sugar levels as given below : $67,69,74,73,70,70,71,67,73,74,73,75,69,72,70,70,72,70,73,74$. Make a frequency table.
2. The marks obtained by 30 students of a class in a test out of 10 marks are as follows :
4,6,5,1,5,4,3,6,8,10,7,1,8,5,4,9,7,10,3,2,4,5,3,6,7,8,4,10,3,9
Make a frequency distribution table for the above data. Use the table to find :
(i) The number of students passed, if the minimum pass marks are $40 \%$.
(ii) How many students failed ?
(iii) How many students secured the highest marks?
(iv) How many students secured more than $60 \%$ marks?
[Hint. Pass marks $=40 \%$ of $10=4,60 \%$ of $10=6]$.
3. The weight (in $\mathrm{kg}$ ) of 30 students of a class are $50,49,45,49,49,50,50,54,55,44,44,42,44,56,57$, $49,49,42,41,50,50,50,57,45,45,45,50,54,43$ and 49 .
Prepare a frequency table for the above data and answer the following questions :
(i) What is the least weight?
(ii) Find the number of students having the least weight in the above data.
(iii) Find the number of students having the maximum weight in the above data.
(iv) Which weight do the maximum number of students have ?
4. The value of $\pi$ up to 50 decimal places is given below :
$3.141592653589793238462643383279502888419716939937510$
Write the frequencies of the following digits in the decimal part of the above number.
(i) 2
(ii) 3
(iii) 5
(iv) 6
(v) 9
(vi) 1
5. Fill in the blanks:
(i) The difference between the maximum and the minimum observations in a data is called the of the data.
(ii) The number of observations in a particular class interval is called the of the class interval.
(iii) The range of the data $15,13,14,17,19,16,14,15$ is
6. Fill in the blanks in the following table :
| Weights in kg | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Class Marks |
[Hint. Class mark for Ist class interval $=\frac{10+20}{2}=\frac{30}{2}=15$. Similarly, the class marks of other class intervals are obtained]
7. For each set of data, make up a tally table, using the groupings suggested and complete the frequency column.
(a) The number of tomatoes picked from tomato plants.
$18,31,25,16,21,20,34,7 \quad$ Suggested grouping
$19,18,24,26,30,21,26,18 \quad 0-4,5-9,10-14,15-19, \ldots \ldots$
$28,31,11,25,33,23,17,24$
(b) The number of books on 18 of the shelves in a college library.
$35,42,43,31,27,39,30,45,37$ Suggested grouping
$33,36,26,30,29,38,36,34,43 \quad 1-25,26-30,31-35,36-40, \ldots . .$
8. The following are the monthly rents (in rupees) of 30 shops:
$42,49,37,82,37,75,62,54,79,84,75,63,44,74,36,69,54,48,74,39,48,45,61,71,47,38,80,51,31,43$
Using the class interval of equal width in which one class interval being $40-50$ (excluding 50 ), construct a frequency table for the above data.
9. Construct a frequency table for the following marks obtained by 45 students using equal class intervals, one of them being $16-24$ ( 24 not included).
$12,35,6,10,8,24,37,32,61,52,63,7,41,48,15,16,25,29,62,40,33,46,18,20,34,28,24,56,55,12,50,56,48,47,38,26,60,42,39,40,43,25,13,46,20$.
10. The following list shows the weights in $\mathrm{kg}$ of the 22 boys students in a class.
$\begin{array}{llllll}37.48 & 61.93 & 58.72 & 49.78 & 51.70 & 68.10 \\ 49.87 & 38.75 & 69.10 & 65.39 & 36.49 & 65.62 \\ 54.63 & 46.17 & 48.80 & 57.35 & 62.25 & \\ 38.50 & 62.82 & 59.73 & 56.60 & 50.15 & \end{array}$
[Hint. Since observations like $37.48,62.25,59.73$, do not fit in any intervals, the class intervals have to overlap in such a way that all values fit in. You may take the intervals as $35-40,40-45,45-50$, $65-70 .]$
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