Question 1

SS/N is called the:

Accepted Answer

SS/N (sum of squares divided by total number of observations) is known as variance. It is a measure of how spread out the data is from the mean.

Question 2

Professor Jones has given a statistics test to her class. After grading the tests she reports to the class that the mean score was a 99 and the standard deviation was 0. The class will be very happy because:

Accepted Answer

A standard deviation of 0 indicates that every student in the class received a score of 99. This means that everyone performed extremely well and achieved the highest possible score.

Question 3

The mean of the scores 3, 6, 7, 8, 1 is:

Accepted Answer

The mean is calculated by adding all the scores together and dividing by the number of scores: (3 + 6 + 7 + 8 + 1) / 5 = 25 / 5 = 5.

Question 4

The square root of the variance is called the:

Accepted Answer

The square root of the variance is the standard deviation, which represents the typical or average distance of each data point from the mean. Option A (squared deviation) and Option C (sum of squared deviations) are not correct as they do not involve taking the square root of the variance. Option B (average squared deviation) is close to the correct answer but does not use the specific term "standard deviation."

Question 5

The most frequently occurring score in a distribution is the:

Accepted Answer

The mode is defined as the score that occurs most frequently in a distribution. Therefore, it is the best choice for the most frequently occurring score. The median is the middle score in a distribution and the arithmetic average (or mean) is the sum of all scores divided by the number of scores in a distribution. These measures may not necessarily capture the most frequently occurring score.

Question 6

The measure of variability that reflects the difference between the largest and smallest scores in a distribution is the:

Accepted Answer

The range is the difference between the largest and smallest scores in a distribution, so this is the measure of variability that reflects that difference. The other options (standard deviation, sum of squares, and variance) all refer to different calculations of variability that do not directly reflect the range.

Question 7

If two sets of data have the same mean and the same range, they will also have:

Accepted Answer

Having the same mean and range does not guarantee that two sets of data will have the same variance, standard deviation, or sum of squares. These measures depend on the distribution of all data points, not just the extreme values and the average.

Question 8

If you were told that the median of a distribution was greater than the mean, what would that tell you about the shape of the distribution?

Accepted Answer

When the median is greater than the mean, it indicates a negatively skewed distribution, where the tail of the distribution is longer on the left side.

Question 9

One reason to use standard scores instead of raw scores is:

Accepted Answer

Standard scores, such as z-scores or T-scores, allow for the comparison of scores from different distributions by transforming raw scores into a standardized form with a mean of 0 and a standard deviation of 1 or a mean of 50 and a standard deviation of 10, respectively. This transformation enables the comparison of scores across different tests or populations, which is not possible with raw scores. While standard scores can be used to calculate correlation coefficients and compare the standard deviation and mean, these are not the primary reasons why standard scores are used instead of raw scores.

Question 10

What technique can a researcher do to analyze data that is collected on different scales?

Accepted Answer

Linear transformation can be used to standardize the data by converting it to a common scale, such as standard scores, which allows for meaningful comparison and analysis. Summing squares, calculating means, and plotting data on a scatter diagram do not address the issue of different scales of measurement.

Question 11

To express a score in terms of its relative position in a distribution, you use:

Accepted Answer

A standard score, such as a z-score or T-score, expresses a score's relative position in a distribution by measuring its distance from the mean in standard deviation units. This allows for easy comparison and interpretation of scores within a distribution. The other options (sum of squares, variance, mean) do not directly address a score's relative position in a distribution.

Question 12

The average of the squared deviations from the mean is called:

Accepted Answer

The average of the squared deviations from the mean is known as variance.

Question 13

When the independent variable represents a point on a continuum, the pictorial representation of the data should be:

Accepted Answer

When the independent variable represents a point on a continuum, such as time or temperature, the best choice for pictorial representation of the data is a line graph, as it allows for a clear visualization of the trend or pattern over time or the continuum. While a bar graph can also be used, it is not as suitable for showing a continuous trend. A frequency polygon is typically used to show the frequency distribution of data, which may not be as relevant when the independent variable is continuous.

Question 14

Under what conditions would the median, mode, and mean be the same value?

Accepted Answer

When the distribution is normal, the median, mode, and mean will be the same value. In a normal distribution, the data is evenly distributed around the center, which results in the equal value of mean, median, and mode.

Question 15

When the independent variable represents categorical information, the pictorial representation of the data should be:

Accepted Answer

When the independent variable represents categorical information, such as different groups or categories, a bar graph is the most appropriate way to visually represent the data. This is because a bar graph allows for easy comparison between the different categories and shows the frequency or proportion of each category. Line graphs and frequency polygons are better suited for representing continuous numerical data.

Question 16

The measure of central tendency that takes all the scores in a data set into account is the:

Accepted Answer

The mean takes all the scores in a data set into account by adding them together and dividing by the total number of scores. The median only takes into account the middle score(s) in the data set, which may not represent the entire group. The mode only takes into account the most frequent score(s) in the data set, which also may not represent the entire group. The range is a measure of dispersion, not central tendency.

Question 17

What is the median of the following scores: 9, 5, 4, 8, 10, 12?

Accepted Answer

To find the median, we need to first order the scores from least to greatest: 4, 5, 8, 9, 10, 12. The middle two scores are 8 and 9, so we take the average of those two numbers. [(8+9)/2 = 8.5]. Therefore, the median score is 8.5, which is closest to answer choice C, 8.

Question 18

If a group of scores are tightly clustered around the mean, they will have a:

Accepted Answer

If a group of scores are tightly clustered around the mean, this means there is little deviation from the mean, or in other words, a small variance. Therefore, choice B is the best answer. A small median or small N do not necessarily indicate a tight cluster of scores, so choices A and C are not applicable.

Question 19

When graphing measures of central tendency from experimental data, you place the ____ on the x-axis.

Accepted Answer

The independent variable is typically placed on the x-axis when graphing measures of central tendency from experimental data, as it represents the variable that is manipulated or changed to observe its effect on the dependent variable.

Question 20

Which of the following is not a measure of variability?

Accepted Answer

Frequency is a measure of central tendency, showing how often a certain value or group of values occurs in a data set. Range, variance, and standard deviation are all measures of variability, showing how spread out the data is.

Quiz 5: Addressing Cultural and Socioeconomic Diversity