Answers:
mean = 124.375
median = 129.5
mode = none
1st quartile = 116
3rd quartile = 138
IQR = 22
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Step-by-step explanation
We need to sort the data from smallest to largest.
Original data set = {135, 126, 107, 80, 125, 133, 141, 148}
Sorted data = {80, 107, 125, 126, 133, 135, 141, 148}
The sample size is n = 8. This is the number of values in the set.
Because n is even, the median is between the two middle-most values.
n/2 = 8/2 = 4, meaning the median is between slot 4 and slot 5
The values at slots 4 and 5 are 126 and 133 respectively.
The midpoint of which is (126+133)/2 = 129.5 which is the median.
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To get the mean, we add up the values and divide by the sample size.
mean = (sum of the values)/(number of values)
mean = (80+107+125+126+133+135+141+148)/8
mean = 995/8
mean = 124.375
This result is exact and hasn't been rounded.
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The mode doesn't require a calculator. We look for the most frequent or most repeated value. In this data set, each value shows up exactly once. There are no repeated values. This data set has no mode.
Side note: it is possible for a data set to have multiple modes
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Recall the median is 129.5
We'll split the data set into two halves labeled L and U
L = lower set = set of stuff smaller than the median
U = upper set = set of stuff larger than the median
L = {80, 107, 125, 126}
U = {133, 135, 141, 148}
Each smaller subset has 4 items (since n/2 = 8/2 = 4)
The median of set L is (107+125)/2 = 116, which is the value of Q1
Also, the median of set U is (135+141)/2 = 138, which is the value of Q3
Q1 = first quartile
Q3 = third quartile
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We'll use the previous results to calculate the IQR.
IQR = interquartile range
IQR = Q3 - Q1
IQR = 138 - 116
IQR = 22
The IQR on a box-and-whisker plot (aka boxplot) represents the width of the box.