Question 1

The median of the data set is defined as…

Accepted Answer

The median is the exact midpoint of a rank ordered dataset. It is the value that divides the data into two equal halves, with half the data above it and half the data below it.

Question 2

The mode of a data set is the…

Accepted Answer

The mode of a data set is the most frequently observed response or value. It is not necessarily the midpoint, sum or range of the data set.

Question 3

Consider the data set that consists of: 10, 20, 32, 35, 44, 30, 60, 11. The value 31 is the…

Accepted Answer

The median is the middle value of a data set when it is ordered in ascending or descending order. For the given data set (10, 20, 32, 35, 44, 30, 60, 11), when ordered (10, 11, 20, 30, 32, 35, 44, 60), the median is the average of the 4th and 5th values (30 and 32), which is 31. The mean (average) of the data set is not 31, and there is no mode since no number repeats.

Question 4

Which of the following measure(s) are commonly used as "typical" measures of center?

Accepted Answer

The mean, median, and mode are all commonly used as measures of center. The mean is the arithmetic average of the data, the median is the middle value when the data is ordered from smallest to largest, and the mode is the most frequent value. Using all three measures of center can provide a more complete understanding of the data's distribution.

Question 5

Given the dataset, what is x̅? 104, 102, 109, 95, 102, 98, 101, 97, 92, 94, 119, 102

Accepted Answer

To find the mean (x̅) of the dataset, add all the numbers together and then divide by the number of items. The sum of the given numbers is 1215, and there are 12 items. 1215 divided by 12 equals 101.25.

Question 6

If you have a dataset with 95 observations, and you pick one and add 5 to it, which of the following is most likely to change?

Accepted Answer

The mean is affected by changes to individual values, while the median and mode are not. Adding 5 to one observation will change the sum of the data, which will in turn affect the mean. Therefore, the mean is most likely to change.

Question 7

If you have a dataset, and you add 5 to each datapoint, what is likely to occur?

Accepted Answer

Adding a constant value to each data point in a dataset shifts all measures of central tendency (mean, median, and mode) by that constant value. Therefore, if you add 5 to each data point, the mean, median, and mode will all increase by 5 units.

Question 8

In this dataset, one score is missing. However, it is known that the average of the dataset is 60.31. The data values are: 28, 86, 46, 80, 68, 58, 40, 99, 90, 24, 34, 98, X. Find the missing value, X.

Accepted Answer

To find the missing value, X, first calculate the sum of the given numbers excluding X, then use the average formula to solve for X. The sum of the given numbers is 751. Since the average is 60.31 and there are 13 data values, the total sum should be 60.31 * 13 = 784.03. Subtracting the sum of the known values from this total gives X = 784.03 - 751 = 33.

Question 9

A research scientist lost a data point out of 100 observations, but luckily has the median. Of the dataset. He asks one of his research assistants to find the missing data point with the remainder 99 observations and the median. Which of the following is true?

Accepted Answer

The median provides the middle value of a dataset when it is ordered but does not give information about the magnitude of each observation, making it impossible to determine a specific missing data point from the median alone.

Question 10

Imagine in a data set where the smallest value is not the mode. Now imagine if that smallest value decreases by 50. Everything else about the data set remains the same. Which of the following must be true?

Accepted Answer

Since the smallest value is not the mode, decreasing it will have an effect on the mean but not on the mode. As the smallest value decreases, the sum of the values in the dataset will decrease, therefore decreasing the mean. The median may or may not change, depending on the location of the smallest value in the original dataset.

Question 11

In a perfectly uni-modal distribution with perfectly symmetric sides around the mode, which of the following is true?

Accepted Answer

In a perfectly uni-modal distribution with symmetric sides around the mode, the mean, median, and mode share the same value. This is because the distribution is perfectly symmetrical, with an equal number of values above and below the mode, which balances out the effect of any outliers or skewness. Therefore, the measure of central tendency (mean, median, and mode) all share the same value.

Question 12

In a distribution where there is a long tail towards the right side of the mode, which of the following is true?

Accepted Answer

A distribution with a long tail towards the right side of the mode is described as positively skewed or right-skewed, not normal. The mean is more heavily influenced by extreme values in the long tail than the median or mode, contradicting options B and C.

Question 13

In a positively skewed uni-modal distribution, how are the three measures of central tendency most likely arranged??

Accepted Answer

In a positively skewed distribution, the mean is usually greater than the median, which is in turn greater than the mode. This is because the long tail to the right pulls the mean higher than the median and mode.

Question 14

In a unimodal distribution where the mean is much greater than the median and the mode. What which of the following is the distribution of the data more likely to resemble?

Accepted Answer

If the mean is much greater than the median and the mode, it indicates that the data has a few high values that are pulling the mean upwards, causing a longer tail on the right side of the distribution, hence making it positively skewed.

Question 15

Which of the following is false of a normal distribution?

Accepted Answer

A normal distribution does not have outliers on either side of the center, as it is symmetrical. The mean, median, and mode are very close and the distribution is symmetrical around the center. Therefore, statement B is false.

Question 16

For which of the following datasets would a mean not be useful?

Accepted Answer

A mean would not be useful for a categorical variable like favorite music artist.

Question 17

A researcher has an experiment with three conditions that generates data on the number of calories worth of food a participant puts on their plate. Which of the following can she do with this data?

Accepted Answer

The researcher can calculate means, medians, and mode for each condition to get a complete understanding of the distribution of the data and compare them across the conditions. This will provide more information than just using one measure of central tendency.

Question 18

Which of the following correctly describes finding the center of a grouped frequency distribution?

Accepted Answer

Each statement accurately describes aspects of finding the center of a grouped frequency distribution: A) involves calculating midpoints for intervals, B) relates to identifying the mode within grouped data, and C) acknowledges potential discrepancies between grouped and ungrouped data analyses.

Question 19

A trimmed mean is the mean without the top and bottom ______ of the data included in the calculation

Accepted Answer

The answer of A trimmed mean is the mean without...

Question 20

Adolphe Quetelet made which of the following observations about data that permeates the social sciences, even today?

Accepted Answer

Adolphe Quetelet observed that many traits and characteristics that we measure tend to fall on a normal distribution, which is still a widely observed phenomenon in the social sciences today. Option A is true, but is not specifically an observation made by Quetelet. Option B is not entirely accurate, as the mean is influenced more by extreme outliers or skewness in a dataset. Option D is also not true, as most traits and characteristics are not uniformly distributed.

Quiz 4: Measures of Central Tendency: Whats so Average About the Mean