2 Mark Question

Question 12 Marks

Find the mode of 90, 55, 67, 55, 75, 75, 40, 35, 55, 95.

Answer

If the data is arranged in ascending order, it is easy to find the observation
repeating maximum number of times.
Ascending order of given data. 35, 40, 55, 55, 55, 67, 75, 75 90, 95
The observation repeated maximum number of times = 55.
∴mode for the given data is 55.

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Question 22 Marks

Find the median of the data. 30, 25, 32, 23, 42, 36, 40, 33, 21, 43

Answer

Let us write the given observations in the ascending order.
$
21,23,25,30,32,33,36,40,42,43
$
Here number of observations $=10$ which is an even number.
$\therefore$ the 5 th and 6 th numbers are in the middle position.
Those numbers are 32 and 33
$
\therefore \text { median }=\frac{32+33}{2}=\frac{65}{2}=32.5
$

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Question 32 Marks

Find the median of 54, 63, 66, 72, 98, 87, 92.

Answer

Let us write the given observations in the ascending order.
54, 63, 66, 72, 78, 87, 92
Here the 4th number is at the middle position, which is 72
∴Median of the scores = 72

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Question 42 Marks

The weights of 10 students (in kg) are given below:
40, 35, 42, 43, 37, 35, 37, 37, 42, 37. Find the mode of the data.

Answer

Given data in ascending order:
35, 35, 37, 37, 37, 37, 40, 42, 42, 43
∴ The observation repeated maximum number of times = 37
∴ Mode of the given data is 37 kg

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Question 52 Marks

In a basket there are $10$ tomatoes. The weight of each of these tomatoes in grams is as follows:
$60, 70, 90, 95, 50, 65, 70, 80, 85, 95.$
Find the median of the weights of tomatoes.

Answer

Given data in ascending order:
$50, 60, 65, 70, 70, 80 85, 90, 95, 95$
$\therefore$ Number of observations $(n) = 10$ (i.e., even)
$\therefore$ Median is the average of middle two observations
Here, 5th and 6th numbers are in the middle position
$\therefore \text { Median }=\frac{70+80}{2}$
$\therefore \text { Median }=\frac{150}{2}$
$\therefore$ The median of the weights of tomatoes is $75$ grams.

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Question 62 Marks

The marks (out of 100) obtained by 7 students in Mathematics examination are given below. Find the mode for these marks.
99, 100, 95, 100, 100, 60, 90

Answer

Given data in ascending order:
60, 90, 95, 99, 100, 100, 100
Here, the observation repeated maximum number of times = 100
∴ The mode of the given data is 100.

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Question 72 Marks

Find the median of the observations, 59, 75, 68, 70, 74, 75, 80.

Answer

Given data in ascending order:
59, 68, 70, 74, 75, 75, 80
∴ Number of observations(n) = 7 (i.e., odd)
∴ Median is the middle most observation
Here, 4th number is at the middle position, which is = 74
∴ The median of the given data is 74.

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Question 82 Marks

Yield of soyabean per acre in quintal in Mukund’s field for 7 years was 10, 7, 5,3, 9, 6, 9. Find the mean of yield per acre.

Answer

$\begin{aligned} \text { Mean } & =\frac{\text { The sum of all observations in the data }}{\text { Total number of observations }} \\ & =\frac{10+7+5+3+9+6+9}{7} \\ & =\frac{49}{7}\end{aligned}$
Mean = 7
The mean of yield per acre is 7 quintals.

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Question 92 Marks

The value of n upto 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
From this information prepare an ungrouped frequency distribution table of digits appearing after the decimal point.

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Question 102 Marks

In a ‘tree plantation’ project of a certain school there are 45 students of ‘Harit Sena.’ The record of trees planted by each student is given below:
3, 5, 7, 6, 4, 3, 5, 4, 3, 5, 4, 7, 5, 3, 6, 6, 5, 3, 4, 5, 7, 3, 5, 6, 4, 4, 3, 5, 6, 6, 4, 3, 5 ,7, 3, 4, 5, 7, 6, 4, 3, 5, 4, 4, 7.
Prepare a frequency distribution table of the data.

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Question 112 Marks

Complete the following table.

Answer

Let frequency of the class 14 – 15 be x then, from table,
5 + 14 + x + 4 = 35
∴ 23 + x = 35
∴ x = 35 – 23
∴ x = 12

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Question 122 Marks

Classify following information as primary or secondary data.
i. Information of attendance of every student collected by visiting every class in a school
ii. The information of heights of students was gathered from school records and sent to the head office, as it was to be sent urgently.
iii. In the village Nandpur, the information collected from every house regarding students not attending school.
iv. For science project, information of trees gathered by visiting a forest.

Answer

i. Primary data
ii. Secondary data
iii. Primary data
iv. Primary data

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