Find the measures of center—mean, median, and mode—for the given dataset.
10, 17, 11, 24, 12, 7, 15, 17, 20, 5, 11, 21, 16, 17
(2 points)
mean:
; median:
; mode:
To find the mean, add up all the numbers in the dataset and then divide by the total number of values:
Mean: (10 + 17 + 11 + 24 + 12 + 7 + 15 + 17 + 20 + 5 + 11 + 21 + 16 + 17) / 14 = 187 / 14 = 13.36
To find the median, first put the numbers in order:
5, 7, 10, 11, 11, 12, 15, 16, 17, 17, 17, 20, 21, 24
Since there are an even number of values, the median is the average of the middle two numbers:
Median: (12 + 15) / 2 = 27 / 2 = 13.5
To find the mode, determine which number appears most frequently in the dataset:
Mode: 17 (since it appears three times, more than any other number)
Question
Find the quartiles for the given dataset.
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
(2 points)
Q1:
; Q2 or the median:
; Q3:
To find the quartiles for the given dataset, first arrange the numbers in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70
Now, to find the quartiles:
Q1 (25th percentile): The median of the lower half of the data set
- Lower half: 35, 40, 40, 45, 45
- Q1: (40 + 40) / 2 = 80 / 2 = 40
Q2 (50th percentile): The median of the entire data set, which is already calculated as 50.
Q3 (75th percentile): The median of the upper half of the data set
- Upper half: 55, 60, 60, 65, 70
- Q3: (60 + 60) / 2 = 120 / 2 = 60
Therefore, the quartiles for the given dataset are:
Q1: 40
Q2 (Median): 50
Q3: 60
ind these measures of variability for the given dataset: range and IQR.
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44
(1 point)
range:
; IQR:
To find the range and IQR (Interquartile Range) for the given dataset, the quartiles need to be determined first as calculated in the previous response:
Arranged dataset in ascending order:
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44
Q1: 26
Median (Q2): 32
Q3: 34.5
Now, the range is the difference between the maximum and minimum values in the dataset:
Range = Maximum value - Minimum value
Range = 44 - 21 = 23
The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1):
IQR = Q3 - Q1
IQR = 34.5 - 26 = 8.5
Therefore, the measures of variability for the given dataset are:
Range: 23
IQR: 8.5
Use the image to answer the question.
A number line ranges from 60 to 100 in increments of 5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 65 to 70. The second box extends from 70 to 80. A line extends from each end of the box, terminating at 60 on the left and terminating at 100 on the right.
For the given box plot, which measure of center—mean or median—best represents the shape of the distribution? Enter 1 for median or 2 for mean.
(1 point)
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