Question

30, anderson (1999) was interested in the effects of attention load on reaction time. participants in her study received a dual - task procedure in which they needed to respond as quickly as possible to a stimulus while simultaneously paying attention to the sounds of spoken words. she recorded reaction time (in hundreds of milliseconds). below are data like those observed by anderson: 3, 4, 4, 4, 5, 6, 8, 12, 20, 25 a. find the mean, median, and mode. b. based on the relative values of those statistics, what is the shape of the distribution? c. anderson (1999) reported median reaction times. why?

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 10$, and $\sum_{i=1}^{10}x_{i}=3 + 4+4+4+5+6+8+12+20+25=91$. So, $\bar{x}=\frac{91}{10}=9.1$.

Step2: Calculate the median

First, arrange the data in ascending order: $3,4,4,4,5,6,8,12,20,25$. Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is $5$ and the 6th value is $6$. So, the median $M=\frac{5 + 6}{2}=5.5$.

Step3: Calculate the mode

The mode is the most frequently occurring value. In the data set $3,4,4,4,5,6,8,12,20,25$, the value $4$ appears 3 times, more frequently than any other value. So, the mode $Mo = 4$.

Step4: Determine the shape of the distribution

Since the mean ($9.1$) is greater than the median ($5.5$) which is greater than the mode ($4$), the distribution is positively skewed.

Step5: Explain why median was reported

The median is a more robust measure of central tendency than the mean when the data is skewed. In a skewed distribution, extreme values (outliers) can greatly affect the mean. Here, the values $20$ and $25$ are relatively large compared to the other values. The median is not affected by extreme values and gives a better representation of the "typical" value in the data set.

Answer:

a. Mean: $9.1$, Median: $5.5$, Mode: $4$
b. Positively skewed
c. The median is a more robust measure of central tendency in a skewed distribution as it is not affected by extreme values.