Question

a) Explain how you can select a systematic sample of size 7 from a population of size 60. b) Compare between the Range the Interquartile range (IQR). c) Suppose that the blood types of students of the first year in a private collage are distributed as follows. Blood Type A B O AB Number 180 120 150 200 Present the blood type data by using bar and pie charts d) suppose that the grade of semester average of ahmed are as follows semester first second third fourth No. hour 18 21 15 17 average 82.4 85 92.7 90.1 compute the Grade Point Average (GPA) for ahmed

Answer 1

solution:

given data:

systematic sample of size:-

a)

• The population size is N = 60 and the sample size is n = 7.
• Number the population observations from 1 to 60. Divide them into 7 groups.
• Now, 60/7 = 8.57
• Let each group have 8 observations.
• First group will have observations 1, 2, 3, ...,8
• Second will have 9, 10, 11, ..., 16
• ... the 7_th group will have  49, 50, 51, ...,56.
• Select any one observation randomly from the first group Let it be the jth observation (j can be anywhere from 1, 2,...,8).
• Then go on selecting the observations j + 8, j + 2*8, j + 3*8, ..., j + 7*8.
• The observations: j, j + 8, j + 2*8, j + 3*8, ..., j + 7*8 will contribute form the systematic sample.
• For example, let j = 3. Then, the systematic sample will consist of the 7 observations numbered 3, 11, 19, 27, 35, 43 and 51.

b)

• Range is defined as the difference between the largest and the smallest observation in the data.
• It is given by, R = L - S, L beign the largest and S being the smallest observation.
• The interquartlie range is defined as the range of the middle 50% of the data, and thus is is the difference between the third quartile (upper quartile) and the first quartile (lower quartile).
• It is given by IQR = Q₃ - Q₁
• The range takes into account the largest and the smallest observation, thus using the maximum and the minimum of the data. Now these maximum and minimum can also be outliers. They could be far from the most of the data points. Hence range as a measure of dispersion of the population can give an inflated value of dispersion.
• On the other hand, IQR ignores the maximum and the minimum of the data and focuses on the middle 50% of the data. Hence, IQR is less prone to be affected by outliers, if any, in the data.
• Therefore, IQR is a more reliable measure of dispersion than range is.

c)

d)

The GPA is given by

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