Question

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The class marks of a distribution are: 28, 33, 38, 43, 48, 53,58,63,68, 73,78.

Determine the class size, the class limits & true limits.​

Answer 1

Step-by-step explanation:

Given: The class marks of a distribution are: 28, 33, 38, 43, 48, 53,58,63,68, 73,78.

To find:Determine the class size, the class limits & true limits.

Solution:

We know that

Class mark= (Lower limit+upper limit)/2

So,

28=(Lower limit+upper limit)/2

56=(Lower limit+upper limit)

Thus,

First class should be 26-30

Next class will be 31-35.

*We know that if there is gap between upper class limit and lower class limit of consecutive classes,we are using true class limits,by subtracting 0.5 from lower limit and adding 0.5 to the upper limit of the same class.

Table is shown below:

Class Interval Class mark True class limit

26-30 _______28________25.5-30.5

31-35________33________30.5-35.5

36-40________38________35.5-40.5

41-45_________43_______40.5-45.5

46-50________48_______45.5-50.5

51-55_________53_______50.5-55.5

56-60________58_______55.5-60.5

61-65________63_______60.5-65.5

66-70________68_______65.5-70.5

71-75_________73_______70.5-75.5

76-80________78_______75.5-80.5

Hope it helps you.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ The class marks of a distribution are: 28, 33, 38, 43, 48, 53,58,63,68, 73,78.

Here,

↝ The class marks are uniformly arranged.

So, The class size is the difference between any two consecutive class marks.

Therefore, Class size = 33 - 28 = 5

We know,

If m is the class mark and h is its class size, then lower and upper limits of the class interval is given by

$\rm :\longmapsto\:\boxed{ \tt{ \: Lower \: limit \: = \: m \: - \: \frac{h}{2} \: \: }}$

and

$\rm :\longmapsto\:\boxed{ \tt{ \: Upper \: limit \: = \: m \: + \: \frac{h}{2} \: \: }}$

So, using this,

Class Limits are as follow :-

$\begin{gathered}\boxed{\begin{array}{c|c} \bf Class \: marks & \bf Class \: limits \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 28 & \sf 25.5 - 30.5 \\ \\ \sf 33 & \sf 30.5 - 35.5 \\ \\ \sf 38 & \sf 35.5 - 40.5\\ \\ \sf 43 & \sf 40.5 - 45.5\\ \\ \sf 48 & \sf 45.5 - 50.5\\ \\ \sf 53 & \sf 50.5 - 55.5\\ \\ \sf 58 & \sf 55.5 - 60.5\\ \\ \sf 63 & \sf 60.5 - 65.5\\ \\ \sf 68 & \sf 65.5 - 70.5\\ \\ \sf 73 & \sf 70.5 - 75.5\\ \\ \sf 78 & \sf 75.5 - 80.5 \end{array}} \\ \end{gathered}$

Since,

Its an exclusive series, so the true class limits are same as class limits.