3B: Characteristics of the Mean

Assignment3b

3B: Characteristics of the Mean

To study perception, a researcher selects a sample of participants (n =

12

) and asks them to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher asks participants to report when they notice a difference in the weight of the two objects. Below is a list of the difference in weight (in pounds) when participants first noticed a difference. Answer the following questions based on the data given in the table.

4

8

1. State the following values for this set of data:

(a) Mean ______

(b) Median ______

(c) Mode(s) ______

(d) Sk ______

(e) Ku ______

2. What is the shape of this distribution? Hint: Use the values of the mean, median and mode to infer the shape of the distribution.

3. State whether the mean increases, decreases, or has no change in each of the following scenarios.

(a) A 13th value of 8 is added to the data. ______

(b) The value of 12 is removed from the data. ______

(c) The value of 7 is removed from the data. ______

4. State the new value of the mean in each of the following scenarios.

(a) Each value is multiplied by 4. ______

(b) Each value is divided by 2. ______

(c) 8 is added to each value. ______

(d) 4 is subtracted from each value. ______

5. Subtract the mean from each score. What is the sum of the differences?

6. Subtract the mean from each score and square each difference. What is the sum of the squared differences? What do you know about this solution?

7. Choosing an Appropriate Measure of Central Tendency.

Depending on the scale of measurement, indicate the most appropriate measure of central tendency (mean, median or mode) for each of the following dependent variables.

(7a) The age (in years) that participants tried their first cigarette.

(7b) The order in which participants complete an endurance task.

(7c) The number of children in single- or two-parent homes.

(7d) The ranking of the effectiveness of four types of learning exercises.

8. Given the following values of the mean and median, state the likely shape of the distribution and which measure should be used to summarize it.

Shape Measure

(8a) mean = 6, median = 14 ______ ______

(8b) mean = 10, median = 3 ______ ______

(8c) mean = 8, median = 8 ______ ______

9. In a negatively skewed distribution, indicate which measure of central tendency is the highest, in the middle and the lowest. In a positively skewed distribution, indicate which measure of central tendency is the highest, in the middle and the lowest. In a normal distribution, indicate which measure of central tendency is the highest, in the middle and the lowest.

Negative Dist. Positive Dist. Normal Dist.

(a) Highest ______ ______ ______

(b) Middle ______ ______ ______

(c) Lowest ______ ______ ______

10. Weighted mean problem

A neuropsychologist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted (n = 8), morphine-addicted (n = 12), and heroin-addicted rats (n = 6). Mean reaction times in each sample are 11, 18, and 13 seconds, respectively. What is the weighted mean for all three samples? Hint: The overall mean is not 14.0 seconds.

11. SPSS

Compute the mean, median, mode, Sk, Ku and histogram with embedded normal curve using SPSS and the data presented below. Paste results here.

Data:100,100,86,100,101,110,100,100,145,114,101,55,99,103,97,90,100,96,104,100,101,92,108,119,79

(11a) Mean =

(11b) Median =

(11c) Range =

(11d) Sk =

(11e) Ku =

(11f) Sd =

(11g) The distribution shape is normal, positively skewed or negatively skewed? {Select one)

(11h) The distribution is mesokurtic, leptokurtic or playtkurtic? (Select one).

(11i) Paste Histogram here. See instructions below or review supplemental file on Bb Course Doc tab.

To obtain a histogram: SPSS. Go to Analyze; Descriptive Statistics; Frequencies. Move variable name over to Variables box. Click on Statistic command and select mean, median, mode range, skewness and kurtosis. Click Continue.

Click on Chart command; select Histogram and then highlight the ‘little’ box that appears (show normal curve). Click continue, then OK.