Step-by-step explanation:
Bob's points per game are
5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15
Calculating Median:
As the median is the middle number in a sorted list of numbers when there is an odd number of terms.
As the the total number of terms = 37
Therefore, the median is the center term which is 10.
5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15
Calculating Range:
As the given data
5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15
The range is the difference between the highest and lowest values in the data set.
The lowest value is 5
The highest value is 15
The range = 15 - 5 = 10
Calculating the interquartile range (IQR)
The interquartile range is the difference between the third and first quartiles.
- The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers.
So, the bottom half is
5 7 7 7 8 8 8 8 8 9 9 9 9 9 10 10 10 10
The median of these numbers is 8.5
- The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers.
So, the upper half is
10 11 11 11 11 11 12 12 12 12 13 13 13 14 14 14 15 15
The median of these numbers is 12
As
The third quartile is 12
The first quartile is 8.5
Therefore,
The interquartile range = 12 - 8.5 = 3.5
Finding Mode
As the given data
5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15
The mode of a set of data is the value in the set that occurs most often.
So, It is bimodal.
Therefore, the mode is 10.
Finding Mean
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
[tex]Mean=Sum\:of\:terms\:\div Number\:of\:terms[/tex]
[tex]Sum\:of\:terms\:=\:385[/tex]
[tex]Number\:of\:terms\:=\:37[/tex]
[tex]Mean\:=\:\frac{385}{37}=10.4[/tex]
Determining whether the data is symmetrical or non-symmetrical
The data is non-symmetric, they do not have about the same shape on either side of the middle. In other words, if you fold the histogram in half, it does not look about the same on both sides. Please check the histogram attached below.
Calculating Mean Absolute Deviation
The mean deviation is a measure of dispersion, A measure of by how much the values in the data set are likely to differ from their mean.
As the given data
5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15
Population size = 37
[tex]Mean=10.4[/tex]
Mean Absolute Deviation (MAD): 2.0
Keywords: mode, median, mean, non-symmetrical data, range, Interquartile Range (IQR)
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