Question

What is the central tendency—mean, median, and mode of this data set? {3,13,7,5,21,23,39,28,40,26,14,12,56,25,29,31}

a. Mean: 24, Median: 26, Mode: No mode
b. Mean: 25, Median: 26, Mode: 29
c. Mean: 25, Median: 26, Mode: 56
d. Mean: 26, Median: 25, Mode: 29

Answer 1

The central tendency of the given data set is mean: 24.5, median: 24, and there is no mode as no number repeats.

Step-by-step explanation:

To find the central tendency of the data set {3,13,7,5,21,23,39,28,40,26,14,12,56,25,29,31}, we need to calculate the mean, median, and mode. The mean is found by adding all the numbers together and then dividing by the number of values. The median is the middle value when the data set is ordered from least to greatest. If the number of values is even, the median is the average of the two middle numbers. The mode is the number that appears most frequently in the data set.

First, we order the data set: 3, 5, 7, 12, 13, 14, 21, 23, 25, 26, 28, 29, 31, 39, 40, 56.

Next, we calculate the mean: (3 + 5 + 7 + 12 + 13 + 14 + 21 + 23 + 25 + 26 + 28 + 29 + 31 + 39 + 40 + 56) / 16 = 392 / 16 = 24.5.

For the median, as there are 16 numbers, we take the average of the 8th and 9th values: (23 + 25) / 2 = 24.

Finally, we look for the mode. Since no number repeats in this data set, there is no mode.

Therefore, the correct central tendency for this data set is mean: 24.5, median: 24, and mode: No mode.