Two sets of data are shown.
Data Set A: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59
Data Set B: 38, 39, 40, 42, 44, 46, 47, 50, 51, 52
Question
Choose ,begin emphasis,all,end emphasis, the measures which are ,begin emphasis,greater,end emphasis, for data set A than for data set B.
Answer options with 5 options
1.
mean
2.
range
3.
median
4.
standard deviation
5.
interquartile range
The correct answer is:
1. mean
2. range
3. median
4. standard deviation
To determine which measures are greater for data set A than for data set B, we can compare the different measures for both sets.
1. Mean: To find the mean, add up all the numbers in the set and divide by the total number of values.
For Data Set A: (30 + 38 + 42 + 42 + 43 + 47 + 51 + 51 + 57 + 59) / 10 = 461 / 10 = 46.1
For Data Set B: (38 + 39 + 40 + 42 + 44 + 46 + 47 + 50 + 51 + 52) / 10 = 449 / 10 = 44.9
Since the mean for Data Set A (46.1) is greater than the mean for Data Set B (44.9), the answer is option 1: mean.
2. Range: The range is the difference between the highest and lowest values in a set.
For Data Set A: 59 - 30 = 29
For Data Set B: 52 - 38 = 14
Since the range for Data Set A (29) is greater than the range for Data Set B (14), the answer is option 2: range.
3. Median: The median is the middle value of a set when the values are arranged in order.
For Data Set A: In ascending order: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59. The median is the average of the 5th and 6th numbers, which is (43 + 47) / 2 = 45.
For Data Set B: In ascending order: 38, 39, 40, 42, 44, 46, 47, 50, 51, 52. The median is the average of the 5th and 6th numbers, which is (44 + 46) / 2 = 45.
Since the medians for Data Set A and Data Set B are the same (45), the answer is not option 3: median.
4. Standard Deviation: The standard deviation measures the amount of variation or dispersion in a set of values. Calculating the standard deviation is a more complex process that involves finding the mean, finding the difference between each value and the mean, squaring those differences, calculating the mean of the squared differences, and taking the square root.
For Data Set A: The standard deviation is 8.92 (rounded to two decimal places).
For Data Set B: The standard deviation is 4.15 (rounded to two decimal places).
Since the standard deviation for Data Set A (8.92) is greater than the standard deviation for Data Set B (4.15), the answer is option 4: standard deviation.
5. Interquartile Range: The interquartile range is the range of the middle 50% of the values in a set. It is calculated by subtracting the first quartile (25th percentile) from the third quartile (75th percentile).
For Data Set A: The first quartile is 42 and the third quartile is 54. Therefore, the interquartile range is 54 - 42 = 12.
For Data Set B: The first quartile is 40 and the third quartile is 49. Therefore, the interquartile range is 49 - 40 = 9.
Since the interquartile range for Data Set A (12) is greater than the interquartile range for Data Set B (9), the answer is option 5: interquartile range.
To determine which measures are greater for data set A than for data set B, we need to compare the values of each measure for both data sets. Let's look at each option:
1. Mean: To find the mean, add up all the values in the data set and divide by the total number of values. For data set A, the mean would be (30+38+42+42+43+47+51+51+57+59)/10 = 460/10 = 46. For data set B, the mean would be (38+39+40+42+44+46+47+50+51+52)/10 = 449/10 = 44.9. Therefore, the mean for data set A (46) is greater than the mean for data set B (44.9).
2. Range: To find the range, subtract the smallest value from the largest value in the data set. For data set A, the range would be 59 - 30 = 29. For data set B, the range would be 52 - 38 = 14. Therefore, the range for data set A (29) is greater than the range for data set B (14).
3. Median: To find the median, arrange the values in ascending order and find the middle value. If there are two middle values, average them. For data set A, the median would be 47 (since there are 10 values). For data set B, the median would be 44 (also because there are 10 values). Therefore, the median for data set A (47) is greater than the median for data set B (44).
4. Standard Deviation: Calculating the standard deviation involves finding the average of the squared differences between each value and the mean, then taking the square root of that average. The standard deviation for data set A is 8.64, and for data set B, it is 5.26. Therefore, the standard deviation for data set A (8.64) is greater than the standard deviation for data set B (5.26).
5. Interquartile Range: The interquartile range is the difference between the first quartile and the third quartile. To calculate it, first find the median of the lower half (first quartile) and the median of the upper half (third quartile). For data set A, the interquartile range is 51 - 42 = 9. For data set B, it is 47 - 40 = 7. Therefore, the interquartile range for data set A (9) is greater than the interquartile range for data set B (7).
In conclusion, the measures that are greater for data set A than for data set B are: mean, range, median, standard deviation, and interquartile range.