Example 2: The results of mechanical aptitude test are as follows: Length of Tim
ID: 3057368 • Letter: E
Question
Example 2: The results of mechanical aptitude test are as follows: Length of Time (in minutes) 4-9 9-14 14-19 19-24 24-29 29 34 Total Number Cf 15 25 37 45 54 a) What is the first quartile, 25 percentile? 25% of 54 is 13.5, the 13.5th number, when numbers are ordered, is P25, the twenty five percentile. When we consult the cumulative frequency distribution, we note that the twenty five percentile is in the class interval 4-9. We assume that the values falling in an interval are uniformly distributed over the interval. * CW 25(54) 100 15 =4+ 5 = 8.5Explanation / Answer
Length of Time
f
CF
d
fd
4
9
15
15
-2
-30
9
14
7
22
-1
-7
14
19
3
25
0
0
19
24
12
37
1
12
24
29
8
45
2
16
29
34
9
54
3
27
54
18
Mean of d=
0.333333
Here the transformation X to d is
d = (X-16.5)/2
Therefore
Mean of d = (Mean of X -16.5)/2
0.3333333 *2 = (Mean of X -16.5)
a) Mean of X = 16.5 + 0.333333*2 = 17.16666
b) Median = Second Quartile = 19.833
c) Mode = l + h*d1/(d1+d2)
This formula cannot be used since modal class is very first class. So we will apply empirical rule given by
Mean-Mode = 3(Mean-Median)
17.16666 – Mode = 3(17.16666 – 19.833)
Mode = 17.16666+3*(17.16666 – 19.833) = 9.16764
e) Variance of d = 3.44444
But variance is independent of change of origin but depends on scale.
Therefore,
Variance of X = 4 * Variance of d = 4*3.44444 = 13.77778
f) Standard Deviation of X = 3.711843
d) Range = Max-Min = 34-4 =30
e)
Length of Time
f
CF
d
fd
4
9
15
15
-2
-30
9
14
7
22
-1
-7
14
19
3
25
0
0
19
24
12
37
1
12
24
29
8
45
2
16
29
34
9
54
3
27
54
18
Mean of d=
0.333333
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