Aptitude test given

Question

An aptitude test was given to a random sample of 222 people who want to work with computers. The results are show int he chart below, where x is the score (on a 10 point scale) and f is the number of people with this score. x 1 2 3 4 5 6 7 8 9 10 f 9 21 46 51 42 18 12 10 8 5 Assume that the above data represents the entire population of people intending to work with computers.

Answer 1

Score (x)Frequency (f)f·x(x – mean)²·f (used later for variance)
1	9	9	—
2	21	42	—
3	46	138	—
4	51	204	—
5	42	210	—
6	18	108	—
7	12	84	—
8	10	80	—
9	8	72	—
10	5	50	—
Total	222	997	—

Now we can compute some key statistics:

1.) Population Mean (μ):

μ = ∑ f • x = 997⁄222 ≈ 4.49

N

2.) Population Variance (σ²):

We compute using:

σ² = ∑ f (x – μ)²

3.) Population Standard Deviation (σ):

σ = √ σ ²

4.) Median and Mode:

Since this is discrete, we can also determine:

1. Median: the 111th and 112th observation (since N = 222)
2. Mode: the score with highest frequency (x = 4, f = 51)