Question

The following are the grades of 27 students in a statistics exam: 20 28 42 51 54 55 56 57 9 61 62 63 64 65 67 68 69 71 74 75 76 77 79 81 84 86 100 a. The number of classes is 5, construct a frequency table. b. Draw a histogram. c. Construct stem and leaf diagram

Answer 1

solution:

Given grades of 27 students

20 28 42 51 54 55 56 57 59 61 62 63 64 65 67 68 69 71 74 75 76 77 79 81 84 86 100

a) The no.of classes required = 5

Here the range of data = Max-Min = 100 - 20 = 80

Class width = Range/No.of classes = 80/5 = 16

When you consider class width as 16 then value 100 is not included.

So, consider Class width = 17

The required frequency Distribution table is :

----> Count the each grade from given data to corresponding class intervals which is called it's frequency

----> Observe, Lower limit is included but not upper limit of each interval

Grades (Class Intervals )	Frequency
20-37	2
37-54	2
54-71	13
71-88	9
88-104	1
	fi =27

b) The Histogram of given data is:

Taking Grades on X-axis and Frequency on Y-axis

  

c) Stem and Leaf plot : A stem and Leaf plot is a table where each data value is split into 'stem'(The first digit (or) digits) and Leaf usually 'Last digit'

--->So, Keep all tenth (or) First digits in Stem and unit digits in Leaf