Question

Find the correct answer from the alternatives given.
(1) The persons of O– blood group are 40%. The classification of persons based on blood groups is to be shown by a pie diagram. What should be the measures of angle for the persons of O– blood group ?

(A) 114°)

(B) 140°

(C) 104°

(D) 144°

(2) Different expenditures incurred on the construction of a building were shown by a pie diagram. The expenditure Rs 45,000 on cement was shown by a sector of central angle of 75°. What was the total expenditure of the construction ?

(A) 2,16,000

(B) 3,60,000

(C) 4,50,000

(D) 7,50,000

(3) Cumulative frequencies in a grouped frequency table are useful to find . . .

(A) Mean

(B) Median

(C) Mode

(D) All of these

(4) The formula to find mean from a grouped frequency table is $\overline{\mathrm{X}}=\mathrm{A}+\frac{\sum f_i{u}_i}{\sum f_i}\times hg$ In the formula u i = . ..

(A) $\frac{x_i+\mathrm{A}}{g}$

(B) $\left(x_i-\mathrm{A}\right)$

(C) $\frac{x_i-\mathrm{A}}{g}$

(D) $\frac{{\displaystyle \mathrm{A}-x_i}}{{\displaystyle g}}$

(5)

Distance Covered per litre (km)	12 - 14	14 - 16	16 - 18	18 - 20
No. of cars	11	12	20	7

The median of the distances covered per litre shown in the above data is in the group . . . . . .

(A) 12 - 14

(B) 14 - 16

(C) 16 - 18

(D) 18 - 20

(6)

No. of trees planted by each student	1 - 3	4 - 6	7 - 9	10 - 12
No. of students	7	8	6	4

The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .

(A) (4, 8)

(B) (3, 5)

(C) (5, 8)

(D) (8, 4)

Answer 1

(1)
Central angle for O– blood group persons = $\frac{40}{100}\times 360°=144°$
Hence, the correct option is (D).
(2)
Central angle for expenditures incurred on the construction = 75°
$$\begin{gathered} \Rightarrow \frac{\mathrm{Expenditures}\mathrm{on}\mathrm{construction}}{\mathrm{Total}\mathrm{expenditures}}\times 360°=75° \\ \Rightarrow \mathrm{Total}\mathrm{expenditures}=45000\times \frac{360°}{75°} \\ =\mathrm{Rs}216000 \end{gathered}$$
Hence, the correct option is (A).
(3)
Cumulative frequencies in a grouped frequency table are used to find the median of the data.
Hence, the correct option is (B).
(4)
To find mean of a grouped frequency table using $\overline{\mathrm{X}}=\mathrm{A}+\frac{\sum f_i{u}_i}{\sum f_i}\times hg$ .
In this formula, $u_i=\frac{x_i-\mathrm{A}}{g}$

Hence, the correct option is (C).
(5)
Since, the class 16 - 18 has the highest frequency. Thus, the median of the distances covered per litre will be lie in this class.
Hence, the correct option is (C).
(6)
The coordinates of the points to show number of students in the class 4-6 are (5, 8).
Hence, the correct option is (C).