This question tests calculating measures of center like mean, variability like MAD, describing the overall pattern in words, and noting striking deviations such as outliers, gaps, or clusters. Measures include mean (sum/count: 139/7≈19.857≈19.9) and MAD (average of absolute deviations from mean, e.g., deviations sum to ≈7, /7≈1.0). The overall pattern should be in words, like 'heights cluster around 20 cm with small spread.' Striking deviations: none here, as data are close. For this data of 18,19,19,20,20,21,22, correct are mean≈19.9, MAD≈1.0, pattern: cluster around 20 with small spread, no deviations. Common errors: wrong mean, MAD not averaging deviations, pattern not in words, falsely calling extremes outliers. To calculate: sum for mean, find |value-mean| and average for MAD; describe pattern narratively, check for deviations visually or with rules.

This question tests calculating mean and MAD (mean absolute deviation), which measures typical variation from the mean. First, find mean: sum = 10+11+12+12+13+14+15 = 87, so mean = 87/7 ≈ 12.43 messages. For MAD: find each deviation from mean |value - 12.43|: |10-12.43|=2.43, |11-12.43|=1.43, |12-12.43|=0.43, |12-12.43|=0.43, |13-12.43|=0.57, |14-12.43|=1.57, |15-12.43|=2.57. Average these deviations: (2.43+1.43+0.43+0.43+0.57+1.57+2.57)/7 = 10.29/7 ≈ 1.47. The pattern shows values increase steadily from 10 to 15, clustering near 12-13 with no gaps or outliers—15 is only 2.57 units from the mean, well within normal variation. Choice A correctly calculates mean ≈ 12.43 and MAD ≈ 1.47, accurately describing the tight cluster with no striking deviations. Choice B has wrong MAD, C has wrong mean, and D has impossibly small MAD.

This question tests calculating measures of center like median and mean, variability like range, describing the overall pattern in words, and noting striking deviations such as outliers, gaps, or clusters. Measures of center include median (middle value for odd count: 16 here) and mean (sum/count: 163/9≈18.11); variability includes range (40-12=28). The overall pattern should be described in words, like 'most values are in the mid-to-high teens, clustered tightly.' Striking deviations include outliers like 40, far from the rest. For this data of 12,14,15,15,16,16,17,18,40, correct measures are median=16, mean≈18.1, range=28, pattern: most in mid-to-high teens, deviation: 40 is an outlier. Common errors include wrong median by miscounting position, mean arithmetic errors, ignoring outlier in pattern description, or not noting deviations. To calculate: order data, find middle for median, sum and divide for mean, max-min for range; describe pattern in words, scan for outliers or gaps.

This question tests calculating measures of center like median and mean, variability like IQR, describing the overall pattern in words, and noting striking deviations such as outliers, gaps, or clusters. Measures include median (middle for even: average 2 and 2=2), mean (22/10=2.2), IQR (Q3-Q1=3-1=2). The overall pattern: 'most games between 1 and 3 goals, clustered low.' Striking deviation: 7 is an outlier. For this data 0,1,1,1,2,2,2,3,3,7, correct: median=2, mean=2.2, IQR=2, pattern: most 1-3, deviation: 7 outlier. Common errors: wrong IQR calculation, missing outlier, pattern only numbers. To calculate: order, find middles for median, sum/divide mean, quartiles for IQR; describe in words, identify outliers.

This question tests finding the median and range for an even number of values, plus identifying patterns and outliers in running times. First, the data is already ordered: 7, 7, 8, 8, 8, 9, 9, 14. For median with 8 values (even), we average the middle two values (4th and 5th positions): the 4th value is 8 and the 5th value is 8, so median = (8+8)/2 = 8. The range = max - min = 14 - 7 = 7 minutes, showing total spread. Looking at the pattern: seven of the eight times cluster tightly between 7-9 minutes (just a 2-minute span), while one time of 14 minutes is 5 minutes slower than the next slowest time, making it a clear outlier. Choice A correctly identifies median = 8 and range = 7, and accurately describes the pattern with 14 as a striking deviation. Choice B incorrectly calculates median as 8.5 (wrong middle values), C misses the outlier entirely, and D reverses the pattern description.

This question tests calculating measures of center like mean and median, variability like range, describing the overall pattern in words, and noting striking deviations. Measures: mean (15/6=2.5), median ((2+3)/2=2.5), range (4-1=3). Pattern: 'values clustered between 2 and 3, fairly balanced.' Deviations: none. For data 1,2,2,3,3,4, correct: mean=2.5, median=2.5, range=3, pattern: clustered 2-3 balanced, no deviations. Common errors: swapping mean/median, wrong range, falsely identifying outlier. To calculate: sum/divide mean, average middles median, max-min range; describe in words.

This question tests calculating measures like median and range, describing pattern including gaps or clusters. Measures include median (middle) and range (max-min) for spread. For example, in data 10,11,12,20,21,22, median=(12+20)/2=16, range=12, pattern: two clusters with gap 13-19. For this data ordered 4,5,5,6,6,7,20,21,22, median=6 (5th), range=22-4=18, pattern: two clusters (4–7 and 20–22) with large gap between 7 and 20. Common errors include wrong median for odd n, range miscalculation, or missing gaps/clusters in description. To calculate median: order, find middle (odd n=9, 5th). Describe pattern in words noting clusters and gaps specifically.

This question tests calculating measures of center like mean and variability like MAD, describing the overall pattern in words, and noting striking deviations. Measures include mean (sum/count) and MAD (average absolute deviation from mean), showing typical variation. For example, in data 50,52,53,54,55,80, mean ≈ $57.3$, MAD large due to outlier. For this data 14,15,15,16,16,17,17,18,25, mean = $153/9=17$, MAD = $18/9=2$, pattern: most heights 14–18 cm, striking deviation: 25 cm is much taller. Common errors include sum mistakes for mean, MAD miscalculated by not averaging deviations or using wrong mean, pattern not in words, or missing the outlier at 25. To calculate MAD: (1) find mean, (2) compute |value - mean| for each, (3) average them. Describe pattern in words like 'clustered 14-18 with one high', note deviations like outliers visibly far from the cluster.

This question tests calculating measures of center (median) and variability (IQR), describing overall pattern in words, and noting striking deviations. Measures: median with 10 values (even) is average of 5th and 6th values: (7+8)/2=7.5; for IQR with 10 values, Q1 is 25th percentile (between positions 2.5 and 3.5, so between 6 and 6: Q1=6) and Q3 is 75th percentile (between positions 7.5 and 8.5, so between 8 and 9: Q3=(8+9)/2=8.5), giving IQR=8.5-6=2.5≈3. Pattern: most days (9 of 10) show 5-9 messages clustered around median 7.5, forming tight group; striking deviation: 30 messages is extreme outlier, approximately 21 messages above next highest value 9. Choice A correctly identifies median=7.5, IQR=3, describes pattern as "most days are 5-9 messages clustered around 7-9," and notes "30 messages is an outlier." Common errors include: incorrect median (choice B: median=7, choice C: median=8), confusing IQR with range (choice B: IQR=25), or missing the outlier (choice D). Calculating IQR: (1) find Q1=6 and Q3≈8.5, (2) subtract: 8.5-6=2.5≈3. Complete summary must identify 30 as extreme outlier that would dramatically affect mean but not median.

This question tests calculating mean and range, plus describing data patterns when values are fairly evenly distributed. First, find mean: sum = 6+7+7+7+8+8+9+9 = 61, so mean = 61/8 = 7.625 correct answers. The range = max - min = 9 - 6 = 3, showing the total spread. Looking at the pattern: scores are distributed across the range 6-9, with slight clustering at 7 (three occurrences) and pairs at 8 and 9, creating a roughly symmetric distribution centered between 7-8. The value 6 is only 1.625 units below the mean, and 9 is only 1.375 above—neither is striking or unusual in this tight distribution. Choice A correctly calculates mean = 7.625 and range = 3, and accurately describes the clustering pattern with no striking deviations. Choice B incorrectly identifies 6 as striking, C has wrong mean and misidentifies the pattern, and D has wrong mean and describes non-existent clusters.