A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 The IQR is

Question

A researcher has collected the following sample data. The mean of the sample is 5.                              3            5            12            3            2               The IQR is

BlackTom AI · Accepted Answer

We start by restating the problem: a sample has values 3, 5, 12, 3, 2 and a mean of 5 is given. We are asked to find the IQR.

First, we sort the data to understand its distribution: 2, 3, 3, 5, 12.

Next, note that there are multiple conventions for calculating quartiles, especially with small samples. One common approach (the inclusive method for odd n) includes the median in both the lower and upper halves when determining Q1 and Q3.

- With n = 5 and the data sorted as [2, 3, 3, 5, 12], the median (the middle value) is 3.
- If we form the lower half by including the median, we get [2, 3, 3]. The median of this lower half is Q1 = 3.
- If we form the upper half by including the median, we get [3, 5, 12]. The median of this upper half is Q3 = 5.

Now compute the IQR as Q3 − Q1 = 5 − 3 = 2.

Considering the answer options provided (12, 1, 10, 2), this method yields 2, which matches the selected option.

Why this choice might differ from other methods: some textbooks use the exclusive method (excluding the median from the halves), which would give Q1 = 2.5 and Q3 = 8.5, producing IQR = 6. The problem’s option 2 aligns with the inclusive/median-in-half convention, which is a valid and commonly used approach in many introductory statistics settings.

If you’re unsure which convention your course uses, check the instruction on quartile calculations or compute IQR using both methods to see how the value shifts and understand the underlying reason for the difference.

A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 The IQR is

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