Center, Shape, & Spread of Data
Help Questions
SAT Math › Center, Shape, & Spread of Data
A survey of 40 households recorded numbers of pets: 0 pets (6 households), 1 pet (9), 2 pets (11), 3 pets (8), 4 pets (6). What is the median number of pets?
1
1.5
2
2.5
Explanation
The 20th and 21st values in the ordered list both fall in the '2 pets' group, so the median is 2. The other choices come from averaging adjacent categories or selecting the wrong position.
Class A has 12 students with an average score of 78, and Class B has 18 students with an average score of 85. What is the average score of all 30 students combined?
80.8
81.5
82.2
85
Explanation
Compute the weighted mean: $(12 \times 78 + 18 \times 85) / 30 = 2466/30 = 82.2$. The other options use an unweighted average (81.5), reverse the weights (80.8), or ignore one class entirely (85).
The travel times (in minutes) for six commuters are 22, 18, 25, 20, 20, and 24. What is the median travel time?
20
21
21.5
22
Explanation
Ordered data are 18, 20, 20, 22, 24, 25, so the median is the average of the two middle values: $(20+22)/2 = 21$. Choices 20 and 22 pick a single middle value, and 21.5 is the mean of all six times.
Five numbers have a mean of 10. One of the numbers is 4. What is the mean of the other four numbers?
6
9.2
11.5
12.5
Explanation
Total is $5 \times 10 = 50$; subtract 4 gives $50 - 4 = 46$, and $46 \div 4 = 11.5$. The other options come from not subtracting the 4 (12.5), misinterpreting mean as $10 - 4$ (6), or dividing by 5 again after subtraction (9.2).
For the data set -3, 0, 5, 7, 11, each value $x$ is transformed to $y = -2x + 5$. What is the range of the transformed data?
14
18
24
28
Explanation
Multiplying by -2 scales the range by 2 (and flips order), and adding 5 does not change the range, so new range is $2 \times 14 = 28$. The other options ignore one of these effects.
Seven test scores have a mean of 78. One score, 92, was mistakenly recorded as 29. What is the correct mean?
78
79
86
87
Explanation
Correct sum is $7 \times 78 + (92 - 29) = 609$, so the mean is $609 \div 7 = 87$. The other choices reflect not correcting the error or adjusting by the wrong amount.
The mean of 12 numbers is 15, and the mean of 8 different numbers is 21. When all 20 numbers are combined, what is the mean?
17
17.4
18
18.6
Explanation
Combined mean is (12×15+8×21)/20=(180+168)/20=17.4. The other choices come from simple averaging or incorrect weighting.
A class has 10 quiz scores with a mean of 84. After discarding the lowest score of 70, what is the mean of the remaining 9 scores, to the nearest tenth?
84
85.6
86
86.7
Explanation
Total is 10×84=840; removing 70 leaves 770, and 770/9≈85.6. Other choices reflect not adjusting the total correctly or dividing by the wrong count.
The heights (in inches) of eight plants are 60, 62, 65, 65, 66, 68, 70, and 72. What is the median height?
65
65.5
66
66.5
Explanation
For an even number of values, the median is the average of the 4th and 5th values: (65+66)/2=65.5. Other choices pick one of the middle values or average the wrong pair.
The mean of four numbers is 6. When a fifth number is added, the mean becomes 7. What is the fifth number?
9
10
11
12
Explanation
The original sum is 4×6=24 and the new sum is 5×7=35, so the fifth number is 35−24=11. Other choices come from averaging the means or arithmetic errors.