Frequency Distribution And Data Quiz

1) Why is it sometimes easier to use a frequency table to interpret data than to examine the distribution of raw scores?

A frequency table transforms the raw scores by showing the means.

Frequency tables display patterns, organizing the data by how often each score occurs.

Raw scores are not based on the sample.

Raw scores do not represent the data.

A frequency table provides a clear and organized representation of the data by showing how often each score occurs. This allows for easier identification of patterns and trends in the data. On the other hand, raw scores alone do not provide any information about the distribution or patterns in the data. Therefore, using a frequency table is more helpful in interpreting the data compared to examining the distribution of raw scores.

Explanation

A frequency table provides a clear and organized representation of the data by showing how often each score occurs. This allows for easier identification of patterns and trends in the data. On the other hand, raw scores alone do not provide any information about the distribution or patterns in the data. Therefore, using a frequency table is more helpful in interpreting the data compared to examining the distribution of raw scores.

2) A frequency distribution that is bell-shaped, symmetric, and unimodal is called a:

Skewed distribution.

Sampling distribution.

Probability distribution.

Normal distribution.

A frequency distribution that is bell-shaped, symmetric, and unimodal is called a normal distribution. This type of distribution is characterized by having the majority of the data clustered around the mean, with equal amounts of data on both sides. It is often used in statistics and probability to model various phenomena in the natural world.

Explanation

A frequency distribution that is bell-shaped, symmetric, and unimodal is called a normal distribution. This type of distribution is characterized by having the majority of the data clustered around the mean, with equal amounts of data on both sides. It is often used in statistics and probability to model various phenomena in the natural world.

3) A normal distribution is:

Symmetric.

Bell-shaped, symmetric, and unimodal.

Unimodal.

Bell-shaped.

A normal distribution is bell-shaped because it follows a specific pattern where most of the data points cluster around the mean and taper off towards the extremes. It is symmetric because the distribution is evenly balanced around the mean, meaning that the left and right sides of the curve are mirror images of each other. Lastly, it is unimodal because it has a single peak or mode, indicating that there is one most common value or range of values in the data.

Explanation

A normal distribution is bell-shaped because it follows a specific pattern where most of the data points cluster around the mean and taper off towards the extremes. It is symmetric because the distribution is evenly balanced around the mean, meaning that the left and right sides of the curve are mirror images of each other. Lastly, it is unimodal because it has a single peak or mode, indicating that there is one most common value or range of values in the data.

4) In comparing frequency tables with grouped frequency tables for the same set of data, which of the following would be true?

If the data set is large the grouped frequency table would be easier to decipher.

Because of overlapping class intervals, the total frequency for a grouped frequency table would exceed that of a frequency table.

It is generally harder to spot patterns in the data when using a grouped frequency table.

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Explanation

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5) A distribution containing a few extremely small values is likely to create a distribution that is:

Negatively skewed.

Normal.

Positively skewed.

Non-representative.

A distribution containing a few extremely small values is likely to create a distribution that is negatively skewed. This is because the presence of these few extremely small values will pull the tail of the distribution towards the left, causing a longer tail on the left side and a concentration of values on the right side. This results in a distribution that is skewed towards the lower end, with the mean being lower than the median.

Explanation

A distribution containing a few extremely small values is likely to create a distribution that is negatively skewed. This is because the presence of these few extremely small values will pull the tail of the distribution towards the left, causing a longer tail on the left side and a concentration of values on the right side. This results in a distribution that is skewed towards the lower end, with the mean being lower than the median.

6) Imagine a researcher found that 65% of bystanders helped a female who dropped her packages but only 32% helped a male that dropped his packages. What type of graph would be appropriate to display this data?

Bar graph

Frequency polygon

Not enough information is available to answer the question

Histogram

A bar graph would be appropriate to display this data because it allows for a visual comparison between the two groups (bystanders helping a female vs. bystanders helping a male) by using separate bars for each group. The height of each bar represents the percentage of bystanders who helped, making it easy to compare the two percentages and see the difference between them.

Explanation

A bar graph would be appropriate to display this data because it allows for a visual comparison between the two groups (bystanders helping a female vs. bystanders helping a male) by using separate bars for each group. The height of each bar represents the percentage of bystanders who helped, making it easy to compare the two percentages and see the difference between them.

7) A bar graph is usually used with __________ data while a histogram is used with _________ data.

Interval; nominal

Ratio; scale

Nominal; scale

Nominal; ordinal

A bar graph is usually used with nominal data while a histogram is used with scale data. Nominal data refers to categorical data where the values are assigned to different categories or labels. A bar graph represents the frequency or count of each category using bars. On the other hand, scale data refers to numerical data that has a consistent interval between values. A histogram represents the distribution of values in a dataset by dividing the data into intervals or bins and showing the frequency or count of values within each interval using bars.

Explanation

A bar graph is usually used with nominal data while a histogram is used with scale data. Nominal data refers to categorical data where the values are assigned to different categories or labels. A bar graph represents the frequency or count of each category using bars. On the other hand, scale data refers to numerical data that has a consistent interval between values. A histogram represents the distribution of values in a dataset by dividing the data into intervals or bins and showing the frequency or count of values within each interval using bars.

8) Professor Arenas recently administered a statistics exam and was surprised to see that the distribution of scores was negatively skewed. What would a negatively skewed distribution indicate for this example?

That most students did well on the exam but a few did very poorly.

That students were at the extreme; some did very well and others did very poorly.

That most students did poorly on the exam but a few did very well.

That there was very little variation in his class; everyone scored about the same.

A negatively skewed distribution indicates that most students did well on the exam but a few did very poorly. This means that the majority of students scored higher on the exam, while a small number of students scored significantly lower. The skewed distribution suggests that there may have been some factors that affected the performance of a few students, resulting in their poor scores compared to the rest of the class.

Explanation

A negatively skewed distribution indicates that most students did well on the exam but a few did very poorly. This means that the majority of students scored higher on the exam, while a small number of students scored significantly lower. The skewed distribution suggests that there may have been some factors that affected the performance of a few students, resulting in their poor scores compared to the rest of the class.

9) Imagine that you calculated Body Mass Index (BMI) for a group of college students and created the grouped frequency table below:

BMI	Frequency
40-44.99	1
35-39.99	4
30-34.99	6
25-29.99	10
20-24.99	20
15-19.99	3

If you decide to depict this data with a histogram what would be the midpoint for the highest interval?

42.5

40

42.49

44.99

The midpoint for an interval is calculated by finding the average of the lower and upper limits of the interval. In this case, the highest interval is 40-44.99. The lower limit is 40 and the upper limit is 44.99. To find the midpoint, we add the lower and upper limits and divide by 2: (40 + 44.99) / 2 = 42.495, which rounds to 42.5. Therefore, the midpoint for the highest interval is 42.5.

Explanation

The midpoint for an interval is calculated by finding the average of the lower and upper limits of the interval. In this case, the highest interval is 40-44.99. The lower limit is 40 and the upper limit is 44.99. To find the midpoint, we add the lower and upper limits and divide by 2: (40 + 44.99) / 2 = 42.495, which rounds to 42.5. Therefore, the midpoint for the highest interval is 42.5.

10) If students in a college math class are given an exam intended for middle school math students it would probably result in:

A positively skewed distribution.

A ceiling effect.

A normal distribution.

A floor effect.

If college math students are given an exam intended for middle school math students, it is likely that the college students will find the exam too easy and score very high. This would result in a ceiling effect, where most of the scores are clustered at the highest possible score.

Explanation

If college math students are given an exam intended for middle school math students, it is likely that the college students will find the exam too easy and score very high. This would result in a ceiling effect, where most of the scores are clustered at the highest possible score.