Question

If weights (kgs) are 50-52,52-54,54-56,56-58,58-60 and corresponding students are17,35,28,15,5. What are the values of class mark

› 51,53,55,57,59

› 52,54,56,58,60

› 51,55,53,57,59

In above Question if we take assumed mean as 55 and h=2, then what is the value of ∑fu

› 44

› -54

› -44

What is the value of mean weight for above Question.

› 55 kg

› -0.44 kg

› 54.56

› 54.12

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Answer 1

Answers:

Question 1: (a) 51, 53, 55, 57, 59

Question 2: (c) -44

Question 3: (c) 54.56

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Question 1: If weight classes (in kgs) are 50-52, 52-54, 54-56, 56-58, 58-60 and the corresponding students are 17, 35, 28, 15, 5. Which of the following options depict the class mark?

‎

(a) 51, 53, 55, 57, 59

(b) 52, 54, 56, 58, 60

(c) 51, 55, 53, 57, 59

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Solution 1:

We have been given the classes and the respective frequencies, and we're asked to find out the class mark.

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What is the class mark?

Class mark is given by the sum of the lower limit and the upper limit of a particular class divided by 2. It is known as the mid-value of a given class.

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$\boxed{\sf Class \ mark = \dfrac{Lower \ limit + Upper \ Limit}{2}}$

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The lower limit refers to the lowest value of the class, whereas the upper limit refers to the highest value of the same class.

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Using the formula mentioned above we get,

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$\left|\begin{array}{c | c | c}\sf \ Class \ & \sf Frequency & \sf Class mark \\\sf \ 50 - 52 \ & \sf 17 & \sf (50 + 52)/2 = 102/2 = \textsf{\textbf{51}} \\\sf \ 52 - 54 \ & \sf 35 & \sf (52 + 54)/2 = 106/2 = \textsf{\textbf{53}} \\\sf \ 54 - 56 \ & \sf 28 & \sf (54 + 56)/2 = 110/2 = \textsf{\textbf{55}} \\\sf \ 56 - 58 \ & \sf 15 & \sf (56 + 58)/2 = 114/2 = \textsf{\textbf{57}} \\\sf \ 58 - 60 \ & \sf 5 & \sf (58 + 60)/2 = 118/2 = \textsf{\textbf{59}} \\\end{array}\right|$

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Therefore, the correct option is (a) 51, 53, 55, 57, 59.

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Question 2: In the above question, if we take the assumed mean to be 55 and h = 2, what is the value of ∑fu?

(a) 44

(b) -54

(c) -44

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Solution 2:

According to the question,

• Assumed mean (a) = 55

• Height of the class (h) = 2

• ∑fu

‎

And, u = (x - a)/h

$\left|\begin{array}{c | c | c | c }\sf \ Class \ & \sf Frequency \ (f) & \sf Class mark \ (x)& \sf u = (x - a)/h \\\sf \ 50 - 52 \ & \sf 17 & \sf 51 & \sf (51 - 55)/2 = \textbf{-2}\\\sf \ 52 - 54 \ & \sf 35 & \sf 53 & \sf (53 - 55)/2 = \textbf{-1} \\\sf \ 54 - 56 \ & \sf 28 & \sf 55 = a & \sf (55 - 55)/2 = \textbf{0} \\\sf \ 56 - 58 \ & \sf 15 & \sf 57 & \sf (57 - 55)/2 = \textbf{1} \\\sf \ 58 - 60 \ & \sf 5 & \sf 59 & \sf (59 - 55)/2 = \textbf{2} \\\end{array}\right|$

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We've got the value of "u" now, so let's find out the value of fu for each class,

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$\left|\begin{array}{c | c | c | c | c }\sf \ Class \ & \sf Frequency \ (f) & \sf Class mark \ (x)& \sf u = (x - a)/h & \sf \ fu \ \\\sf \ 50 - 52 \ & \sf 17 & \sf 51 & \sf -2 & \sf 17 \times -2 = -34 \\\sf \ 52 - 54 \ & \sf 35 & \sf 53 & \sf -1 & \sf 35 \times -1 = -35 \\\sf \ 54 - 56 \ & \sf 28 & \sf 55 = a & \sf 0 & \sf 0 \\\sf \ 56 - 58 \ & \sf 15 & \sf 57 & \sf 1 & \sf 15 \times 1 = 15 \\\sf \ 58 - 60 \ & \sf 5 & \sf 59 & \sf 2 & \sf 5 \times 2 = 10 \\\end{array}\right|$

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∑fu = (-34) + (-35) + 0 + 15 + 10

∑fu = -69 + 25

∑fu = -44

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Therefore, the correct option is (c) -44

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Question 3: What is the value of mean weight for the above question?

(a) 55 kg

(b) -0.44 kg

(c) 54.46 kg

(d) 54.12 kg

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$\sf \Longrightarrow Mean = a + \dfrac{\Sigma fu}{\Sigma f}$

‎‎

Here,

• a = 55

• ∑fu = -44

• ∑f = 17 + 35 + 28 + 15 + 5

$\sf \Longrightarrow Mean = 55 + \dfrac{-44}{17 + 35 + 28 + 15 + 5}$

‎‎

$\sf \Longrightarrow Mean = 55 + \bigg\{\dfrac{-44}{100}\bigg\}$

‎‎

$\sf \Longrightarrow Mean = 55 + \big\{- 0.44\big\}$

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$\sf \Longrightarrow Mean = 55 - 0.44$

‎‎

$\sf \Longrightarrow \textsf{\textbf{Mean = 54.56}}$

‎‎

Therefore, the correct option is (c) 54.56.

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Answer 2

1]

Given :-

If weights (kgs) are 50-52,52-54,54-56,56-58,58-60 and corresponding students are17,35,28,15,5.

To Find :-

$\sum fu$

Solution :-

Table

$\left\{\begin{array}{ccc}\sf Weight&\sf Frequency\\50-52&17\\52-54&35\\54-56&28\\56-58&15\\58-60&5\end{array}\right\}$

We know that

Class Mark = Lower limit + Upper limit/2

For 50 - 52

Class mark = 50 + 52/2

Class mark = 102/2

Class mark = 51

For 52 - 54

Class mark = 52 + 54/2

Class mark = 106/2

Class mark = 53

For 54 - 56

Class mark = 54 + 56/2

Class mark = 110/2

Class mark = 55

For 56 - 58

Class mark = 56 + 58/2

Class mark = 114/2

Class mark = 57

For 58 - 60

Class mark = 58 + 60/2

Class mark = 118/2

Class mark = 59

Hence

Option A is correct

2]

Given :-

Mean = 55

H = 2

To Find :-

value of ∑fu

Solution :-

$\left\{\begin{array}{ccc}\bf Weight&\bf Frequency&\bf Classmark\\50-52&17&51\\52-54&35&53\\54-56&28&55\\56-58&15&57\\58-60&5&59\end{array}\right\}$

Now,

u = Class mark - Mean/2

For 50 - 52

u = 51 - 55/2

u = -4/2

u = -2

For 52 - 54

u = 53 - 55/2

u = -2/2

u = -1

For 54 - 56

u = 55 - 55/2

u = 0/2

u = 0

For 56 - 58

u = 57 - 55/2

u = 2/2

u = 1

For 58 - 60

u = 59 - 55/2

u = 4/2

u = 2

Now

Σfu = (17 × -2) + (35 × -1) + (28 × 0) + (15 × 1) + (5 × 2)

Σfu = -34 + (-35) + 0 + 15 + 10

Σfu = -69 + 25

Σfu = -44

3]

To Find :-

Mean

Solution :-

Now,

Mean = a + Σfu/Σf

Mean = 55 + (-44)/17 + 35 + 28 + 15 + 5

Mean = 55 - 44/100

Mean = 55 - 0.44

Mean = 54.56