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Maths 2 Marks Questions

P-1 Statistics · Maharashtra Board STD 10 (MSBSHSE - English Medium). 12 questions.

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2 Marks Questions

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12 questions · 1 auto-graded MCQ + 11 self-marked written.

Question 12 Marks
The following table shows the income of farmers in a grape season. Find the mean of their income.
Answer

Mean is given by
Mean $=\frac{\sum x _{ i } f _{ i }}{\sum f _{ i }}$
⇒ Mean = 4410/84
⇒ Mean = 52.5
Now, since the income is given in thousand rupees.
Then, Mean = 52.5 × 1000
⇒ Mean = 52500
Thus, mean income is Rs. 52,500.
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Question 22 Marks
The age group and number of persons, who donated blood in a blood donation camp is given below. Draw a pie diagram from it.
Answer
Let us find the measures of central angles and show them in a table.
Know that,
Measures of central angles $=\frac{\text { No. of persons }}{\text { Total number of persons }} \times 360^{\circ}$

Now we shall show the table into a pie chart.
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Question 32 Marks
Find the correct answer from the alternatives given.

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
First, draw a table converting the given class into continuous class.

Drawing it into a frequency polygon.


So, the coordinates of the points to show number of students in the class 4-6 are (5,8).
Thus, option (C) is correct.
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MCQ 42 Marks
Find the correct answer from the alternatives given.The median of the distances covered per litre shown in the above data is in the group $. . . . .$
 
  • A
    $12-14$
  • B
    $14-16$
  • ✓
    $16-18$
  • D
    $18-20$
Answer
Correct option: C.
$16-18$

Here, $( n / 2)^{\text {th }}=(50 / 2)^{\text {th }}=25^{\text {th }}$ term
$cf =23<25 $
$\Rightarrow \text{ Median class }=16-18$
Median class is the next class of interval of cumulative frequency.
Thus, option $(C)$ is correct.
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Question 52 Marks
Find the correct answer from the alternatives given.
The formula to find mean from a grouped frequency table is $\bar{x}=A \frac{\sum f_i u_i}{\sum f_i} \times h g$
In the formula $u_i$ =……
A. $\frac{X_1+A}{g}$
B. $(x,-A)$
C. $\frac{X_1-A}{g}$
D. $\frac{A-X_i}{g}$
Answer
Among the given option, $\left(X_i-A\right) / g$ is the correct option.
Where $X_i=$ values in the given data corresponding to $i^{\text {th }}$ position.
$ A=\text { Assumed mean }$
$\mathrm{g}=\text { class size }$
Thus, (C) is the correct option.
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MCQ 62 Marks
Find the correct answer from the alternatives given.
Cumulative frequencies in a grouped frequency table are useful to find . . .

 
  • A
     Mean
     
  • B
     Median
     
  • C
    Mode
     
  • D
     All of these
Answer
The cumulative frequency of a set of data or class intervals of a frequency table is the sum of the frequencies of the data up to a required level. It can be used to determine the number of items that have values below a particular level.
Mean is simple or arithmetic average of a range of values or quantities, computed by dividing the total of all values by the number of values. And The mode of a set of data values is the value that appears most often.
While, median is the middle value of the set of ordered data. The position of the median is given by ${(n + 1)/2}^{th}$ value, where n is the number of values in a set of data.
So, the formula can be applied in the cumulative frequency in an arranged data to find the median.
Thus, (B) is the correct option.
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Question 72 Marks
The following table shows the income of farmers in a grape season. Find the mean of their income.
Income
(Thousand Rupees)		20-3030-4040-5050-6060-7070-80
Farmers101115161814
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Question 82 Marks
The age group and number of persons, who donated blood in a blood donation camp is given below. Draw a pie diagram from it.
Age group (Yrs)20-2525-3030-3535-40
No. of persons80603525
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MCQ 92 Marks
No. of trees planted by each student3-Jan6-Apr9-Jul12-Oct
No. of students7864

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 . . . .
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MCQ 102 Marks
Find the correct answer from the alternatives given.

Distance Covered per litre (km)14-Dec14-1616-1818-20
No. of cars1112207

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

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