Question

In: Statistics and Probability

The table below shows marks scored by 42 students in a French test 35   49   69  ...


The table below shows marks scored by 42 students in a French test

35   49   69   57   58   75   48
40   46   86   47   81   67   63
56   80   36   62   49   46   26
41   58   68   73   65   59   72
64   70   64   54   74   33   51
73   25   41   61   56   57   28

I.   Group the data into 7 classes and make a frequency distribution             (3mks)
II.   Calculate:          
(i)   Mean mark                                   (2mks)
(ii)   Median mark                                   (2mks)
(iii)   Mode                                        (2mks)
(iv)   Standard deviation                               (3mks)
III.   Comment on the distribution                                (1mk)

Solutions

Expert Solution

For the data, we have the minimum value is 25 and the maximum value is 86. The difference or the range is

86-25=61. We need to have 7 classes which implies that the class interval is 61/7=8.714~9. Therefore, we shall make class interval 9 with seven classes starting from 25.

I. The frequency distribution is :

The frequency distribution is therefore

Class Interval Frequency
25-34 4
35-44 5
45-54 8
55-64 12
65-74 9
75-84 3
85-94 1
Total 42

II. For calculating various quantities, we make the following table:

Marks Marks^2
35 1225
40 1600
56 3136
41 1681
64 4096
73 5329
49 2401
46 2116
80 6400
58 3364
70 4900
25 625
69 4761
86 7396
36 1296
68 4624
64 4096
41 1681
57 3249
47 2209
62 3844
73 5329
54 2916
61 3721
58 3364
81 6561
49 2401
65 4225
74 5476
56 3136
75 5625
67 4489
46 2116
59 3481
33 1089
57 3249
48 2304
63 3969
26 676
72 5184
51 2601
28 784
Total 2363 142725

i). Mean mark is given by

ii). Median mark:It is the average of 21st and 22nd observations in ascending order. ie

iii). Mode: Is that value in the data that occurs the most in the data.

In the given data, the values that occured most is 56, 57 and 58 which occurred 2 each respectively and the first number is 56.

iv). Standard deviation:

The variance is calculated by

  

  

Therefore the standard deviation  

III.

The frequency distribution is given by

From the chart we can see that the distribution is fairly symmetrical around the mean and the median is also close to the mean.


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