PSYC 3002 – Week 2 Assignment – Measures of Central Tendency and Variability

PSYC 3002 – Week 2 Assignment – Measures of Central Tendency and Variability

The mean is the score located at the center of a distribution, also referred to as the average. Both the mean and the average can be computed in the same The mean is calculated by adding up the scores and then dividing by the number of scores you added (Heiman, p. 41, 2015). The man tells me that participants in the sample walked on average 162.6 minutes.

Median- the score in the middle of the data set when numbers are in numerical order (Laureate Education, 2015). The median is another name for the score at the 50^th percentile (Heiman, p.40, 2015). The median falls at the 50^th. If there is an even data set, there will be 2 middle numbers. Those 2 middle numbers will be added together and divided by 2, and the midpoint will be found. I calculated the median as 185. Since the median is 185, this means that 50% of the employers walked less than 185 minutes, and 50% walked more than 185 minutes.

Mode- the most frequent score in the data set. The mode in this data set is 122 because it appears in the data more than the other scores in the data set. The mode is a score that has the highest frequency in the data (Heiman, 2015). The model is found by looking at the data set and finding which value appears in the data most frequently. The model is 122, which means that the employees walked 122 minutes more than any other score (Laureate Education, 2015).

PSYC 3002 – Week 2 Assignment – Measures of Central Tendency and Variability

The range is the distance between the highest and lowest score (Laureate Education, 2015f). “The descriptive statistic that indicates the distance between the two most extreme scores in a distribution is called the range” (Heiman, p. 55, 2015). The range for this data set is 168. The range is calculated by subtracting the lowest score of 52 from 220, the highest score. The range means that the employees who walked the most did so 168 times more than those who walked the least.

Deviation– is the distance of the highest score from the mean. In this data set, the mean is 162.6. To find the deviation, you would find the highest score in the data set, which is 220 and subtract. The deviation of the highest score from the mean would be 220-162.6, which equals 57.4. According to (Laureate Education, 2015), you should “Always subtract the score from the mean when computing a score’s deviation.” The answer is 57.4 for the deviation of the highest score from the mean. This says that the highest number of minutes walked deviates from 57.4 minutes.

Estimated population standard deviation– is the variability in a population based on the variability in a sample (Laureate Education, 2015). It also equals the average of all the deviations from the mean and is the square root of the estimated variance. The estimated population standard deviation is 49.989. We know that the standard deviation is the square root of the variance, and the square root of 2499.2 is 49.989. This means that the frequency of the employees who walked was more than the typical number of times they walked in a week by 49.98 times.

∑X2– ∑ is computed when each raw score is squared, then added together. The symbol ∑X2 indicates to find the sum of the squared X’s (Heiman, p.62, 2015). Each raw score is squared, then added together (Laureate Education, 2015). The answer is 576260.

(∑)2– indicates finding the squared sum of X. Is calculated by working inside the parenthesis (Heiman, p.62, 2015). All the raw scores are added up, and the sum is squared (Laureate Education, 2015). The answer is the mean computed in SPSS is 162.7500. The standard deviation computed in SPSS is 49.80158.

PSYC 3002 – Week 2 Assignment – Measures of Central Tendency and Variability

For this sample, the mean will increase. When there is one less data score, the mean will increase. The mode will stay the same since the highest frequency does not change. The deviation of the highest score from the mean increased as the mean.

The distribution forms a normal curve because extremely high and low scores are relatively infrequent (Laureate Education, 2015). Scores closer to the middle score are more frequent, and the middle score occurs most frequently (Laureate Education, 2.1, 2015). The low-frequency, extremely low and extremely high scores are in the tails of a normal distribution.

Reference List

Heiman, G. (2015). Behavioral Sciences STAT (2^nd ed.). Stamford, CT: Cengage.

Laureate Education (Producer). (2015l). SPSS tutorial: Description statistics [Video file]. Baltimore, MD: author.

Laureate Education (Producer). (2015e). Measures of central tendency [Video file]. Baltimore, MD: Author.

Laureate Education (Producer). (2015f). Measures of variability [Video file]. Baltimore, MD: Author.

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Computation and Interpretation. Use SPSS to compute the following measures of central tendency, then interpret what those results tell you about the sample:

Mean

Median

Mode

Range

Standard deviation

In your written answer document, include the following for each statistic:

The answer you obtained from SPSS

An interpretation of what each statistic tells you about the variable