Figure 3.1.G shows a stem and leaf plot of the ratings (out of 100 ) of an actor's performance in different movies.Stem Leaf4 1 75 2 3 46 4 4 77 1 3 5 68 79 0Figure 3.1.G: Performance rating of an actor.Here 6 | 4 means Rating of 64What is the Inter Quartile Range (IQR)? (Correct to 1 decimal point accuracy.)
Question
Figure 3.1.G shows a stem and leaf plot of the ratings (out of 100 ) of an actor's performance in different movies.Stem Leaf4 1 75 2 3 46 4 4 77 1 3 5 68 79 0Figure 3.1.G: Performance rating of an actor.Here 6 | 4 means Rating of 64What is the Inter Quartile Range (IQR)? (Correct to 1 decimal point accuracy.)
Solution
To calculate the Inter Quartile Range (IQR), we first need to find the values of the first quartile (Q1) and the third quartile (Q3).
The data from the stem and leaf plot is as follows:
41, 47, 52, 53, 54, 64, 64, 71, 73, 75, 76, 87, 90
There are 13 data points.
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To find Q1 (the first quartile), we use the formula (n+1)/4, where n is the number of data points. So, (13+1)/4 = 3.5. This means that Q1 is halfway between the third and fourth data points, which are 52 and 53. So, Q1 = 52.5.
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To find Q3 (the third quartile), we use the formula 3*(n+1)/4. So, 3*(13+1)/4 = 10.5. This means that Q3 is halfway between the tenth and eleventh data points, which are 75 and 76. So, Q3 = 75.5.
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Finally, to find the IQR, we subtract Q1 from Q3. So, IQR = Q3 - Q1 = 75.5 - 52.5 = 23.0.
So, the Inter Quartile Range (IQR) is 23.0.
Similar Questions
Figure 3.1.G shows a stem and leaf plot of the ratings (out of 100 ) of an actor's performance in different movies.Stem Leaf4 1 75 2 3 46 4 4 77 1 3 5 68 79 0Figure 3.1.G: Performance rating of an actor.Here 6 | 4 means Rating of 64What is the median rating, if 3 points are added to all of his ratings and then converted to 10 points. (Correct up to 2 decimal point accuracy.)
The Interquartile Range (IQR), a fundamental measure in Descriptive Statistics, is best described as: A. The difference between the highest and lowest values in a dataset. B. The variance between the mean and the median of a dataset. C. The gap between the upper (Q3) and lower quartile (Q1) of a dataset. D. The summation of the dataset's upper (Q3) and lower quartile (Q1).
In a box plot, what does the interquartile range (IQR) represent?Question 5Answera.Range of the middle 50% of the datab.Sum of the first and third quartilesc.Difference between the maximum and minimum valuesd.Average of all data points
The interquartile range (IQR) is defined to be the difference between the two quartile values.TrueFalse
The interquartile range IQR is a useful measure of data spread utilizing relative position. Recall that the IQR is the difference between the third and first quartiles.IQR = Q3 − Q1We previously found Q1 = 6 from Q3 = 9.5. Use these values to calculate the IQR.IQR = Q3 − Q1 = − 6 =
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