Measure Of Central Tendency

1. Wes has kept a daily record of his phone text messages for several days. Which data set has a mode of 18?

13, 15, 17, 17, 19, 21, 23, 23

5, 7, 6, 18, 20, 18, 23, 25

20, 21, 7, 16, 15, 18, 2, 9

21, 4, 7, 9, 4, 20, 5, 3, 18

The data set 5, 7, 6, 18, 20, 18, 23, 25 has a mode of 18. The mode is the value that appears most frequently in a data set. In this case, the number 18 appears twice, which is more than any other number in the set. Therefore, 18 is the mode of this data set.

Explanation

The data set 5, 7, 6, 18, 20, 18, 23, 25 has a mode of 18. The mode is the value that appears most frequently in a data set. In this case, the number 18 appears twice, which is more than any other number in the set. Therefore, 18 is the mode of this data set.

2. Find the mean, median, mode, and range of the data set.
3, 5, 8, 3, 4, 2, 3

Mean: 4, Median: 4, Mode: 3, Range: 5

Mean: 4, Median: 3, Mode: 3, Range: 5

Mean: 4.5, Median:3, Mode: 7, Range: 5

Mean: 5, Median: 3, Mode: 3, Range: 5

The mean is calculated by finding the sum of all the numbers in the data set and dividing it by the total number of values. In this case, the sum of 3, 5, 8, 3, 4, 2, and 3 is 28. Dividing 28 by 7 (the total number of values) gives a mean of 4. The median is the middle value when the data set is arranged in ascending order. Arranging the numbers in ascending order gives 2, 3, 3, 3, 4, 5, and 8. The middle value is 3, so the median is 3. The mode is the number that appears most frequently in the data set. In this case, 3 appears three times, which is more than any other number, so the mode is 3. The range is the difference between the largest and smallest values in the data set. The largest value is 8 and the smallest value is 2, so the range is 8 - 2 = 6. Therefore, the correct answer is Mean: 4, Median: 3, Mode: 3, Range: 5.

Explanation

The mean is calculated by finding the sum of all the numbers in the data set and dividing it by the total number of values. In this case, the sum of 3, 5, 8, 3, 4, 2, and 3 is 28. Dividing 28 by 7 (the total number of values) gives a mean of 4. The median is the middle value when the data set is arranged in ascending order. Arranging the numbers in ascending order gives 2, 3, 3, 3, 4, 5, and 8. The middle value is 3, so the median is 3. The mode is the number that appears most frequently in the data set. In this case, 3 appears three times, which is more than any other number, so the mode is 3. The range is the difference between the largest and smallest values in the data set. The largest value is 8 and the smallest value is 2, so the range is 8 - 2 = 6. Therefore, the correct answer is Mean: 4, Median: 3, Mode: 3, Range: 5.

3. The number of boats going through a strait was recorded during 10 days as follows:
36, 41, 58, 45, 36, 39, 52, 40, 43, 47
Suppose the 47 should be 94 instead. Which measure of central tendency would change?

Mean

Median

Mode

All of the above

The mean is the average value of a set of numbers. In this case, the mean of the original set of numbers is calculated by adding up all the numbers and dividing by the total count (10). If the number 47 is changed to 94, it significantly affects the sum of the numbers and therefore the mean. The mean would change because the new sum would be higher, resulting in a higher average value. Therefore, the correct answer is mean.

Explanation

The mean is the average value of a set of numbers. In this case, the mean of the original set of numbers is calculated by adding up all the numbers and dividing by the total count (10). If the number 47 is changed to 94, it significantly affects the sum of the numbers and therefore the mean. The mean would change because the new sum would be higher, resulting in a higher average value. Therefore, the correct answer is mean.

4. Officer Jackson is researching recorded speeds on a particular roadway. Which data set has a
mean closest to 34 mph?

34, 34, 36, 37, 38, 44, 45

29, 28, 31, 34, 39, 40, 50

30, 29, 28, 40, 55, 24, 25

14, 34, 25, 36, 38, 39, 54

The data set with a mean closest to 34 mph is 14, 34, 25, 36, 38, 39, 54.

Explanation

The data set with a mean closest to 34 mph is 14, 34, 25, 36, 38, 39, 54.

5. A quiz is given to 33 students. Scores on the quiz can range from 1 to 10. Based on the results below, which conclusion can be drawn regarding the measures of central tendency?
1, 1, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9

The median is lower than the mean or mode.

The mode is lower than the mean or median.

The mean is lower than the mode or median.

The mean, medihttp://www.proprofs.com/quiz-school/submit2.phpan, and mode are approximately equal.

The given data set is not symmetrical, as there are more occurrences of the numbers 5, 6, 7, and 8 compared to the other numbers. The mode represents the most frequently occurring value, which in this case is 5. The median is the middle value when the data set is arranged in ascending order, which is also 5. However, the mean is calculated by summing up all the values and dividing by the total number of values. Since there are more occurrences of the numbers 5, 6, 7, and 8, the mean is pulled towards these higher values, making it higher than the mode and median. Therefore, the correct conclusion is that the mean is lower than the mode or median.

Explanation

The given data set is not symmetrical, as there are more occurrences of the numbers 5, 6, 7, and 8 compared to the other numbers. The mode represents the most frequently occurring value, which in this case is 5. The median is the middle value when the data set is arranged in ascending order, which is also 5. However, the mean is calculated by summing up all the values and dividing by the total number of values. Since there are more occurrences of the numbers 5, 6, 7, and 8, the mean is pulled towards these higher values, making it higher than the mode and median. Therefore, the correct conclusion is that the mean is lower than the mode or median.