Given is a graphical display of Quiz Scores, now we need to find which estimates of the mean and median are most plausible.
Now clearly the the graphical display is a histogram with classes of length 2 in the x axis and the corresponding frequencies in the y axis. Now let us re-make the frequency distribution which corresponds to the histogram.
No. | Class Boundary | Frequency | |
Lower | Upper | ||
1 | 4 | 6 | 1 |
2 | 6 | 8 | 1 |
3 | 8 | 10 | 0 |
4 | 10 | 12 | 1 |
5 | 12 | 14 | 2 |
6 | 14 | 16 | 3 |
7 | 16 | 18 | 5 |
8 | 18 | 20 | 4 |
Total | 17 |
Now let us calculate the median of this frequency distribution. For that we prepare a cumulative frequency column of less than type.
No. | Class Boundary | Frequency | Cumulative Frequency | |
Lower | Upper | |||
1 | 4 | 6 | 1 | 1 |
2 | 6 | 8 | 1 | 2 |
3 | 8 | 10 | 0 | 2 |
4 | 10 | 12 | 1 | 3 |
5 | 12 | 14 | 2 | 5 |
6 | 14 | 16 | 3 | 8 |
7 | 16 | 18 | 5 | 13 |
8 | 18 | 20 | 4 | 17 |
Total | 17 |
Now median is given by,
Now here the median class is, n/2=17/2=8.5 i.e the 7th class is the median class.
Hence,
Now mean is given by,
where,
So we make a class mark column our frequency distribution. Now class mark is the average of the upper and class boundary.
No. | Class Boundary | Class Mark(xi) | Frequency(fi) | xi*fi | |
Lower | Upper | ||||
1 | 4 | 6 | 5 | 1 | 5 |
2 | 6 | 8 | 7 | 1 | 7 |
3 | 8 | 10 | 9 | 0 | 0 |
4 | 10 | 12 | 11 | 1 | 11 |
5 | 12 | 14 | 13 | 2 | 26 |
6 | 14 | 16 | 15 | 3 | 45 |
7 | 16 | 18 | 17 | 5 | 85 |
8 | 18 | 20 | 19 | 4 | 76 |
Total | 17 | 255 |
.
Hence Median=16.2 and Mean=15.
Hence the most plausible option is third option Median=16 and Mean=14.3. Since they are close to the exact mean and median.
For this graphical display of Quiz Scores, which estimates of the mean and median are most...
1. Consider the following POPULATION of quiz scores {18, 23, 7,
20, 15, 12, 6, 23, 17, 16 }
Compute the following: the mean ,μ, the variance, σ2, the
standarddeviation, σ.
State the mode, if one exists __________
ApplytheEmpiricalRuleatthe95%level.
What percentage of these Quiz Scores actually lie within the
interval found in part c? _________________________
II. Again consider the given Quiz Scores: {18, 23, 7, 20, 15,
12, 6, 23, 17, 16 }
Determine Q1, the median, and Q3:
Draw...
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In R please
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