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Question

Ex2) The following data represent the top 25 ranked college by SAT scores (out of 2400)

 

1544	1500	1480	1455	1440
1515	1490	1475	1455	1440
1505	1489	1470	1450	1435
1505	1485	1460	1445	1435
1500	1480	1460	1440	1435

 

(a) Construct a frequency, relative frequency distribution, and cumulative relative frequency of data (5 classes). Also, find the class midpoint and class boundary

 

Class Limit	Frequency	R.F	Cum. Freq.	Cum. R. F
Total	25	1	25	1

 

Answer 1

Step 1:

Class width should be an odd number.

Round the class width to nearest odd number.

For instance: Get the first class limit add the class width to lowest value.

1435 + 21 = 1456.

Continue the process.

Step 2:

Class boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence.

Each class has an upper and lower class boundary.

 

For instance : For the first class :1435 - 1456

The lower class boundary is the mid point between 1434 and 1435.

(1434 + 1435)/2 = 1434.5

The upper class boundary is the mid point between 1456 and 1457.

(1457 + 1458) = 1456.5

Continue the process.

Step 3:

 

Answer 2

Contd...

Class limit	Frequency	Class mid point	Class boundaries	R.F	Cum.frq	CumR.F
1435-1456	10		1434.5-1456.5		10
1457-1478	4		1456.5-1478.5		14
1479-1500	7		1478.5-1500.5		21
1501-1522	3		1500.5-1522.5		24
1523-1544	1		1522.5-1544.5		25
Total	25			1	25	1