Find the interquartile range given these data points: 57,66,69,71,72,73,74,77,78,7879,79,81,81,82,83,83,88,89,94.
When I used the TI-84 calculator, I got ...
Q1=72.5
Q3=82.5
IQR=Q3-Q1=82.5-72.5=10
But....
When I created a stem and leaf plot I found that
Q2= (78+79)/2 =78.5
Q1=72
Q3=83
IQR= 83-72=11
So is it 10 or 11?
Did I do something wrong when using the stem and leaf plot?
To find the interquartile range (IQR), you need to first determine the values of the first quartile (Q1) and the third quartile (Q3). The IQR is then calculated by subtracting Q1 from Q3.
In your case, you obtained different values for Q1 and Q3 when using two different methods - the TI-84 calculator and the stem and leaf plot. This discrepancy can occur due to rounding or different methods used for calculating quartiles.
The TI-84 calculator uses a method called the "Tukey method" for quartiles, which calculates Q1 and Q3 by interpolating between neighboring data points. This approach can result in more precise values.
On the other hand, the stem and leaf plot method involves sorting the data points and finding the median (Q2), which is the same as the second quartile. Q1 is then determined as the median of the lower half of the data, and Q3 is found as the median of the upper half of the data.
In your case, it seems that the TI-84 calculator and the stem and leaf plot method yielded slightly different values for Q1 and Q3, resulting in different values for the IQR.
To decide which value is correct, it is essential to consider the underlying assumptions and the context of your analysis. If you need a more precise and accurate estimation, you can rely on the TI-84 calculator method. However, if you want to use a simple visual method, the stem and leaf plot approach would suffice.
Both values, 10 and 11, are relatively close, so the difference is likely negligible and may not significantly affect your analysis.
Based on your calculations, you have correctly found the values for the quartiles using both methods. However, in this case, the discrepancy between the two methods is due to the way the interquartile range is defined.
The interquartile range (IQR) is the range between the first quartile (Q1) and the third quartile (Q3). So, in your first calculation using the TI-84 calculator, you found Q1 = 72.5 and Q3 = 82.5, resulting in an IQR of 82.5 - 72.5 = 10.
In your second calculation using the stem and leaf plot, you found Q1 = 72 and Q3 = 83, which gives an IQR of 83 - 72 = 11.
Both calculations are correct, as the exact values of the quartiles can vary slightly depending on the method used to calculate them. Therefore, it is not necessarily wrong to have a discrepancy in the IQR based on different calculation methods.