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 12.5th value lies between the 12th and the 13th value. The 12th value in the data is 53 and the 13th value in the data is 55. Thus, the first quartile (Q1) is:
Now, the 37.5th value lies between the 37th and the 38th value. The 37th value in the data is 82 and the 38th 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 11th value is 52. Thus, the 22nd
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,
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