Center, Shape, & Spread of Data
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ACT Math › Center, Shape, & Spread of Data
What is the median of the data set 14, 18, 12, 10, 16?
12
14
16
18
Explanation
The median is the middle value when data is sorted in order. First, sort the data: [10, 12, 14, 16, 18]. Since there are 5 values (odd count), the median is the middle (3rd) value $= 14$. The median provides a measure of central tendency that is not affected by extreme values.
What is the median of the data set 9, 5, 12, 8, 7?
7
8
9
12
Explanation
The median is the middle value when data is sorted in order. First, sort the data: [5, 7, 8, 9, 12]. Since there are 5 values (odd count), the median is the middle (3rd) value = 8. The median is resistant to extreme values and represents the central tendency.
What is the mode of the data set 7, 9, 7, 5, 9, 9?
5
7
9
None
Explanation
The mode is the value that appears most frequently in the dataset. Counting frequencies: 7 appears 2 times, 9 appears 3 times, 5 appears 1 time. Since 9 appears most frequently (3 times), the mode is 9. Choice B gave 7, which appears only twice.
What is the mean of the data set 3, 7, 5, 10, 8?
6.6
6.8
7
7.6
Explanation
The mean is calculated by finding the sum of all values and dividing by the count. Sum = 3 + 7 + 5 + 10 + 8 = 33. Count = 5 values. Mean = 33 ÷ 5 = 6.6. Choice B gave 7, which would be incorrect arithmetic.
What is the range of the data set 14, 27, 19, 33, 22?
14
19
22
33
Explanation
The range is calculated as the difference between the maximum and minimum values. First, identify the maximum value (33) and minimum value (14). Range = maximum - minimum = 33 - 14 = 19. The range provides a simple measure of how spread out the data values are.
What is the median of 15, 9, 7, 5, 13?
7
9
11
13
Explanation
The median is the middle value when data is sorted in order. First, sort the data: [5, 7, 9, 13, 15]. Since there are 5 values (odd count), the median is the middle (3rd) value $= 9$. The median divides the dataset into two equal halves.
What is the mode of the data set 3, 8, 3, 5, 9, 3, 2?
3
5
8
9
Explanation
The mode is the value that appears most frequently in the dataset. Counting frequencies: 3 appears 3 times, 8 appears 1 time, 5 appears 1 time, 9 appears 1 time, 2 appears 1 time. Since 3 appears most frequently, the mode is 3.
What is the range of the data set 11, 14, 18, 21, 25?
11
14
18
25
Explanation
The range is calculated as the difference between the maximum and minimum values. First, identify the maximum value (25) and minimum value (11). Range = maximum - minimum = 25 - 11 = 14. The range indicates the total span of values from the smallest to the largest data point.
What is the median of the data set 34, 23, 28, 29, 22?
23
28
29
34
Explanation
The median is the middle value when data is sorted in order. First, sort the data: [22, 23, 28, 29, 34]. Since there are 5 values (odd count), the median is the middle (3rd) value = 28. The median represents the value that divides the ordered dataset in half.
Which best describes the shape of the distribution of the data 1, 2, 2, 3, 4, 4, 4, 5, 6?
Bimodal
Symmetric
Skewed right
Skewed left
Explanation
To determine skewness, examine the distribution of values and where the tail extends. The data [1, 2, 2, 3, 4, 4, 4, 5, 6] has most values clustered on the lower end with fewer values extending toward higher numbers. This creates a right-skewed (positively skewed) distribution where the tail extends to the right. Choice B (skewed left) would have the opposite pattern.