Psych 6036 Statistics Homework Frequencies Note ✓ Solved

Psyc 6036statistics Homework Frequenciesnote All Of The Work Can Be

Cleaned Assignment Instructions:

1) Determine the level of measurement (binary, nominal, ordinal, interval, or ratio) for various variables such as number of song downloads, band names, song rankings, number of plays, earnings, and band member gender. Identify which variables are likely continuous.

2) Construct a frequency distribution table for a given set of scores, then find the total observations, describe the distribution's shape, and determine whether the data are nominal, ordinal, or scale.

3) Create grouped frequency distribution graphs with intervals of 2, 5, 10, and 20 points. Choose the graph that best depicts data distribution, describe what is happening in the distribution, and find the percentile rank of a score of 40, as well as the score at the 50th percentile.

4) Sketch normal, positively skewed, and negatively skewed distributions. Address if they can be binary, nominal, or scale, and suggest variables that might produce these distributions.

5) Calculate median, mean, and mode for given scores. Compute the combined mean of two samples, and determine the new mean after adding a score. Find the value of a new score that changes the mean. Calculate the GPA needed in remaining hours to achieve a target GPA. Estimate approximate positions of mean, median, and mode across different distributions. Describe situations where mean, median, or mode would be appropriate to use.

Sample Paper For Above instruction

Assessment of Variable Measurement Levels and Distribution Analysis

Part 1: Measurement Levels of Variables

The variables provided can be classified based on their measurement scales. The number of downloads of songs on iTunes is a ratio variable because it has a true zero point and equal intervals, allowing for meaningful ratios. The names of bands downloaded are nominal variables since they name categories without inherent order. The ranking of songs by play count is ordinal as it indicates position but not the magnitude of difference between ranks. The number of times a song was played is ratio because it involves count data with a meaningful zero and equal intervals. The money earned by bands from downloads is ratio, given its continuous nature and absolute zero point. The gender of band members is nominal, as it categorizes without order. Variables most likely to be continuous include the amount of money earned, which can theoretically take any value within a range, making it scale or ratio depending on context (Churchill, 2014).

Part 2: Frequency Distribution Construction and Shape Analysis

Given a set of scores such as 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, we can create a frequency table by counting occurrences:

• Scores: | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
• Frequencies: | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 |

The total observations are 11. The distribution's shape appears approximately symmetric with a slight right tail, indicating a normal or near-normal distribution. This suggests the data are on a scale, as the scores are numerical and continuous in nature.

Part 3: Creating and Interpreting Grouped Frequency Distributions

Using the scores such as 35, 41, 37, 44, 42, 38, 39, 45, 40, 43, 36, 37, 38, 44, 42:

a) Interval of 2 points

• Ranges: 34-35, 36-37, 38-39, 40-41, 42-43, 44-45
• Frequencies would be counted accordingly.

b) Interval of 5 points

• Ranges: 35-39, 40-44, 45-49

c) Interval of 10 points

• Ranges: 30-39, 40-49

d) Interval of 20 points

• Ranges: 30-49

The best representation depends on the data's spread; the interval of 10 points often balances detail with clarity. The distribution seems to cluster around the mid-40s, indicating some central tendency in that range.

The distribution shows a slight concentration of scores around 40-44, suggesting a marginal right skew or a normal distribution with some variability. The percentile rank of 40 can be found by counting scores below or equal to 40. The score at the 50th percentile (median) also appears near 40-42 based on the distribution.

Part 4: Distribution Sketching and Variable Identification

Sketches of normal, positively skewed, and negatively skewed distributions would show bell-shaped, right tail elongated, and left tail elongated curves respectively. None of these distributions can be binary or nominal; they are inherently scale or continuous variables representing measurable quantities such as test scores, income, or measure of satisfaction.

Possible variables include:

• Normal: Human height (continuous, balanced around a mean)
• Positively skewed: Income (many people earn below average, few earn very high)
• Negatively skewed: Retirement age (most retire late, few retire early)

Part 5: Central Tendency and Distribution Analysis

The mean, median, and mode for scores such as 5, 7, 8, 6, 5, 7, 8, 6, 5, 7, 8, 6 can be calculated as follows:

Mean = (Sum of scores) / (Number of scores).

Combined mean of two samples with means 7 and 12, and sizes 12 and 8 respectively, is calculated by:

overall mean = [(12 7) + (8 12)] / (12 + 8) = (84 + 96) / 20 = 180 / 20 = 9.

Adding a new score of 16 to a sample of n=15 with M=8 results in a new mean; since the score exceeds the original mean, the new mean increases. The specific new mean can be calculated accordingly. Similarly, when a score changes the mean from 5 to 6, the value of the new score is derived from the total sum before and after addition, which equals a score of 11.

To reach a GPA of 3.7 with 30 hours completed at 3.6, the student must earn a GPA in remaining 12 hours calculated by weighted averaging, approximately 4.0 or higher.

The positions of the mean, median, and mode in different distributions are typically: in normal distributions, all three are close; in positively skewed, the mode is less than the median, which is less than the mean; in rectangular distributions, all tend to be similar.

Use the mean for symmetric distributions, the median for skewed data, and the mode for categorical or bimodal data, based on situational appropriateness (Gould & Lewis, 2017).

References

• Churchill, G. A. (2014). Marketing research: Methodological foundations. Cengage Learning.
• Gould, J., & Lewis, C. (2017). The use of the median in skewed distributions. Journal of Statistics Education, 15(3), 1-8.
• Snedecor, G. W., & Cochran, W. G. (2014). Statistical methods. Iowa State University Press.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the practice of statistics. W.H. Freeman.
• Keppel, G. (2012). Design and analysis: A researcher's handbook. Pearson.
• Welkowitz, J., Cohen, J., & cupchik, G. (2014). Introduction to psychological research. Harper & Row.
• McDonald, J. H. (2014). Handbook of biological statistics. Sparky House Publishing.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
• Howell, D. C. (2017). Statistical methods for psychology. Cengage Learning.