4. Consider the histogram in Figure 2 that depicts a random sample of n 30 obser
ID: 3075071 • Letter: 4
Question
4. Consider the histogram in Figure 2 that depicts a random sample of n 30 observations. Use this histogram to answer the question below. Histogram of x Figure 2: Histogram of n- 30 observations to be used for Question 4 (a) One of the statements below is correct. Which is it? i. The sample median falls in the interval [0, 0.5) ii. The sample median falls in the interval [0.5, 1.0) iii. The sample median falls in the interval 1.0, 1.5) iv. The sample median falls in the interval 1.5, 2.0) v. The sample median falls in the interval [2.0, 2.5) vi. The sample median falls in the interval [2.5, 3.0) vii. The sample median is greater than or equal to 3. (b) Provide a clear justification of why you chose your statement above. You statement must be clear enough to convince someone who understands the basics of medians and histograms to be convinced that you are correctExplanation / Answer
(a)
Correct option:
(ii) The sample median falls in the interval [0.5,1.0).
(b)
From the given histogram the following Frequency Distribution is formed:
Class Linits Mid point (x) Frequency (f) Cumulative Frequency (CF)
0 - 0.5 0.25 11 11
0.5 - 1.0 0.75 5 16
1.0 - 1.5 1.25 4 20
1.5 - 2.0 1.75 2 22
2.0 - 2.5 2.25 1 23
2.5 - 3.0 2.75 2 25
3.0 - 3.5 3.25 4 29
3.5 - 4.0 3.75 0 29
4.0 - 4.5 4.25 1 30
Median = Size of N/2 th item = 30/2 = 15th item.
From the above Cumulative Frequency Distribution, we note that it is reached at 16 and corresonding class interval is 0.5 - 1.0. i.e., Class [0,5, 1.0).
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