Question

consider the following sample data, which represent weights walnuts in grams: {7, 12.2, 12.3, 12.5, 13.8, 13.9, 14.2, 14.3, 14.5, 14.8, 14.9, 15.7, 16.1, 16.2, 18.1, 18.3, 18.6, 18.6, 18.7, 19.5 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. part 3 of 6 now give the mode of the data set. if there is more than one, write them in order, separated by commas. part 4 of 6 finally, give the midrange of the data set. part 5 of 6 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will probably be skewed to the right. the distribution will probably be skewed to the left. the distribution will be roughly symmetric.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 20$ and $\sum_{i=1}^{20}x_{i}=7 + 12.2+12.3+12.5+13.8+13.9+14.2+14.3+14.5+14.8+14.9+15.7+16.1+16.2+18.1+18.3+18.6+18.6+18.7+19.5 = 290.2$. So $\bar{x}=\frac{290.2}{20}=14.51$.

Step2: Calculate the median

Since $n = 20$ (an even - numbered data - set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. The 10th value is $14.8$ and the 11th value is $14.9$. Median $=\frac{14.8 + 14.9}{2}=14.85$.

Step3: Find the mode

The mode is the value that appears most frequently. In this data - set, $18.6$ appears twice and all other values appear only once, so the mode is $18.6$.

Step4: Calculate the mid - range

The mid - range is $\frac{\text{min}+\text{max}}{2}$, where $\text{min}=7$ and $\text{max}=19.5$. Mid - range $=\frac{7 + 19.5}{2}=13.25$.

Step5: Determine the shape of the distribution

Since the mean ($14.51$) is less than the median ($14.85$), the distribution will probably be skewed to the left.

Answer:

Part 1: $14.51$
Part 2: $14.85$
Part 3: $18.6$
Part 4: $13.25$
Part 5: The distribution will probably be skewed to the left.