Question

question 31 compute the mean, median, and mode for the set of scores presented in the following frequency - distribution table. 2 pts

Explanation:

Step1: Calculate the sum of scores times frequencies

The scores ($X$) and frequencies ($f$) are: $X = [1,2,3,4,5,6,7]$ and $f=[3,2,1,1,3,4,1]$. The sum $\sum(X\times f)=1\times3 + 2\times2+3\times1 + 4\times1+5\times3+6\times4+7\times1=3 + 4+3 + 4+15+24+7 = 60$.

Step2: Calculate the total frequency

The total frequency $N=\sum f=3 + 2+1+1+3+4+1 = 15$.

Step3: Calculate the mean

The mean $\bar{X}=\frac{\sum(X\times f)}{N}=\frac{60}{15}=4$.

Step4: Calculate the median

Since $N = 15$ (an odd - numbered data set), the median position is $\frac{N + 1}{2}=\frac{15+1}{2}=8$. Counting the cumulative frequencies: $3$ (for $X = 1$), $3+2 = 5$ (for $X = 2$), $5 + 1=6$ (for $X = 3$), $6+1 = 7$ (for $X = 4$), $7+3 = 10$ (for $X = 5$). The 8th value falls within the $X = 5$ category, so the median is $5$.

Step5: Calculate the mode

The mode is the score with the highest frequency. The highest frequency is $4$ which corresponds to $X = 6$, so the mode is $6$.

Answer:

Mean: $4$, Median: $5$, Mode: $6$