QUESTION IMAGE
Question
jill and her friends went miniature golfing for her birthday. they kept track of how many putts each person took on the final hole. this line plot shows the results.
final hole
line plot with number of putts on x - axis from 1 to 7 and green dots representing data
complete the sentences.
the distribution of the number of putts is best described as dropdown. so, the dropdown is a more appropriate measure of variation than the dropdown.
- First, analyze the distribution of the number of putts from the line plot. The data has a longer tail on the right (higher number of putts) or left? Wait, looking at the plot: the number of dots (frequency) increases as the number of putts increases? Wait, no: at putt 1: 1 dot, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5? Wait, no, maybe I misread. Wait, the x - axis is number of putts (1 - 7), and the dots: for putt 1: 1 dot, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5? Wait, no, actually, the left - most (putt 1) has 1, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5? Wait, no, maybe the other way: the frequency increases as the number of putts increases, so the distribution is skewed left? Wait, no, skewed left means the tail is on the left (low values), skewed right means tail on the right (high values). Wait, if the frequency is higher for higher putt numbers, then the tail is on the left (low putt numbers have lower frequency). So the distribution is skewed left? Wait, no, let's count the number of dots:
Putt 1: 1
Putt 2: 1
Putt 3: 1
Putt 4: 2
Putt 5: 3
Putt 6: 4
Putt 7: 5
Wait, no, that can't be. Wait, maybe the plot is: putt 1: 1, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5? No, maybe I got it wrong. Wait, actually, the line plot: the number of dots (frequency) for each putt:
Looking at the plot, the left - hand side (low putt numbers) has fewer dots, and as putt numbers increase, the number of dots increases. So the distribution is skewed left? Wait, no, skewed left: mean < median, tail on left. Skewed right: mean > median, tail on right. Wait, if the frequency is higher for higher values, the tail is on the left (low values), so it's skewed left? Wait, no, let's think again. Let's list the frequencies:
Putt 1: 1
Putt 2: 1
Putt 3: 1
Putt 4: 2
Putt 5: 3
Putt 6: 4
Putt 7: 5
Wait, no, maybe the plot is:
Putt 1: 1
Putt 2: 1
Putt 3: 1
Putt 4: 2
Putt 5: 3
Putt 6: 4
Putt 7: 5
Wait, the total number of dots: 1 + 1+1 + 2+3 + 4+5 = 17? Wait, no, maybe I miscounted. Alternatively, maybe the plot is:
Putt 1: 1
Putt 2: 1
Putt 3: 1
Putt 4: 2
Putt 5: 3
Putt 6: 4
Putt 7: 5? No, that seems off. Wait, maybe the correct way: the number of dots for each putt:
Putt 1: 1
Putt 2: 1
Putt 3: 1
Putt 4: 2
Putt 5: 3
Putt 6: 4
Putt 7: 5? No, maybe the plot is actually with putt 1: 1, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5. So the frequency increases as the number of putts increases. So the distribution is skewed left (because the tail is on the left - low putt numbers have lower frequency).
When a distribution is skewed, the interquartile range (IQR) is a better measure of variation than the range, because the range is affected by outliers or the skewed tail, while IQR is resistant to skewness. Also, for skewed distributions, the median is a better measure of center, but here we are talking about variation.
Wait, the first blank: the distribution is skewed left (or skewed right? Wait, maybe I made a mistake. Let's re - examine: if the frequency is higher for lower putt numbers? Wait, no, maybe the plot is:
Putt 1: 4 dots, putt 2:4, putt 3:4, putt 4:3, putt 5:2, putt 6:1, putt 7:1? No, the original plot: the left - most (putt 1) has 1, putt 2:1, putt 3:1, putt 4:2, putt 5:3, putt 6:4, putt 7:5. So the frequency increases with the number of putts, so the tail is on the left (low putt numbers have lower frequency), so the distribution is skewed left.
For a skewed distribution, the interquartile range (IQR) is a more appropriate measure…
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The distribution of the number of putts is best described as skewed left. So, the interquartile range is a more appropriate measure of variation than the range.
(For the blanks: first blank: skewed left; second blank: interquartile range; third blank: range)