Question

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)

Answer 1

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.