Mathematics Data Analysis: Sorting, Frequency Distribution, Class Limits, Quartiles, And Percentiles

Step 1: Data Entry

a.Step 1: Data Entry

                                                                                              

Step 2: Sorting

                                                             

Step 3: Sorted data on Marks

                                                                                                        

The completely sorted data is given in the following table:

Student No.	Marks in Maths	Student No.	Marks in Maths	Student No.	Marks in Maths	Student No.	Marks in Maths	Student No.	Marks in Maths
2	22	1	52	43	55	48	67	32	87
39	23	50	53	45	55	11	72	49	87
3	26	6	55	30	60	22	72	28	91
47	32	7	55	5	62	21	73	37	91
15	33	8	55	17	62	29	73	20	93
35	33	9	55	13	63	18	74	38	93
14	35	10	55	34	63	19	82	27	95
25	38	24	55	12	66	26	82	31	95
4	39	41	55	23	66	33	82	40	99
46	42	42	55	16	67	36	82	44	99

b.The range is given by the formula:

Range = Maximum Value – Minimum Value

            = 99 – 22

            = 77

3.

                                                                                                       

                                                                                                                       = 62

Mode = The value which has occurred the most number of times

                                                                                                                       = 55.

4.Range = 77

Number of classes = 8

Therefore, class width

                                                                                                                

Step 2: Sorting

5.To find the class limits, the minimum limit is considered as 21 as the minimum marks obtained is 22.

The class width is 10.

Therefore, the lower limit of the 8 classes will be estimated as follows:

21

21 + 10 = 31

31 + 10 = 41

41 + 10 = 51

51 + 10 = 61

61 + 10 = 71

71 + 10 = 81

81 + 10 = 91

91 + 10 = 101

The upper limit of the classes is calculated by subtracting 1 from the lower limit of the next class. Thus, the upper limit of the classes is given as follows:

31 – 1 = 30

41 – 1 = 40

51 – 1 = 50

61 – 1 = 60

71 – 1 = 70

81 – 1 = 80

91 – 1 = 90

101 – 1 = 100

This will be the last class as no values are larger than 100 in the dataset. Therefore, the class limits can be written as:                                                                                                                                                                                                                           

6.To find the class boundaries, the difference between the upper boundary of one class and the lower boundary of the next class is divided by 2. The value thus obtained is added to the upper class boundary and subtracted from the lower class boundary to obtain the class boundaries.

Upper limit of first class = 30

Lower limit of the second class = 31

Therefore, the class limits will be altered by =

                                                                                                                       

Step 3: Sorted data on Marks

Thus, the class boundaries are given by:

                                                              

7.The frequency distribution and the cumulative frequency are given in the following table:

                                                              

8.The stem and leaf diagram of the data is given in the following table:

                                                           

 9.Quartiles can be estimated using the following formula:

                                                                                    

 Now, the 12.5^th value lies between the 12^th and the 13^th value. The 12^th value in the data is 53 and the 13^th value in the data is 55. Thus, the first quartile (Q1) is:

                                                      

Now, the 37.5^th value lies between the 37^th and the 38^th value. The 37^th value in the data is 82 and the 38^th value in the data is 82. Thus, the third quartile (Q3) is:

                                                                                                   

 The interquartile range (IQR) = Q3 – Q1 = 82 – 54 = 28

10.Percentiles can be estimated using the following formula

                                                                       

Now, the 11^th value is 52. Thus, the 22^nd

                                                                              

11.

            Outliers are the points that lies 1.5 IQR below the first quartile and 1.5 IQR above the third quartile. Therefore,

Lower outlier range =

Upper outlier range =

            There are no values outside the ranges of the outliers in the given data on marks of mathematics. Thus, there are no outliers to the data.

12. 

                                                      

Therefore,