what is the interquartile range of this data?\n6\n8\n9\n20\nnumber of coins in collection\n0 4 8 12 16 20 24…
what is the interquartile range of this data?\n6\n8\n9\n20\nnumber of coins in collection\n0 4 8 12 16 20 24 28 32 36 40
Answer
Explanation:
Step1: Find Q1 and Q3
The data set from the number - line: 4, 16, 32, 40. First, find the median of the lower half (Q1) and upper half (Q3). Since there are 4 data points, the median of the whole set is the average of the 2nd and 3rd ordered values. The lower half is 4, 16 and the median (Q1) is $\frac{4 + 16}{2}=10$. The upper half is 32, 40 and the median (Q3) is $\frac{32+40}{2}=36$.
Step2: Calculate the inter - quartile range (IQR)
The formula for IQR is $IQR = Q3 - Q1$. Substitute Q1 = 10 and Q3 = 36 into the formula: $IQR=36 - 10=26$. But if we assume the data points are more spread out on the number - line and we consider the box - and - whisker plot concept more accurately, if we assume the lower quartile (Q1) is 8 and the upper quartile (Q3) is 20.
Step3: Re - calculate the inter - quartile range (IQR)
Using the formula $IQR = Q3 - Q1$, substitute Q1 = 8 and Q3 = 20. So, $IQR=20 - 8 = 12$. However, if we assume the correct Q1 = 8 and Q3 = 16 (a more likely interpretation based on the number - line if we consider the quartile division), then $IQR=16 - 8=8$.
Answer:
8