Question

consider the following sample data, which represent weights walnuts in grams: { 10.6, 10.9, 11.6, 11.7, 12.9, 13.5, 13.5, 14, 14, 14, 14.4, 14.6, 14.9, 15.4, 16.3, 16.6, 17.2, 17.2, 17.8 , 18.5 }. 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 be roughly symmetric. the distribution will probably be skewed to the left. the distribution will probably be skewed to the right.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 20$ and $x_{i}$ are the data - points.
$\sum_{i=1}^{20}x_{i}=10.6 + 10.9+11.6+11.7+12.9+13.5+13.5+14+14+14+14.4+14.6+14.9+15.4+16.3+16.6+17.2+17.2+17.8+18.5 = 287.5$
$\bar{x}=\frac{287.5}{20}=14.375$

Step2: Recall the rule for 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 ordered data set: $\{10.6, 10.9, 11.6, 11.7, 12.9, 13.5, 13.5, 14, 14, 14, 14.4, 14.6, 14.9, 15.4, 16.3, 16.6, 17.2, 17.2, 17.8, 18.5\}$
The 10th value is 14 and the 11th value is 14.4. Median $=\frac{14 + 14.4}{2}=14.2$

Step3: Determine the mode

The mode is the value that appears most frequently in the data set. The number 14 appears 3 times, more frequently than any other number, so the mode is 14.

Step4: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$.
Minimum value $=10.6$, Maximum value $=18.5$
Mid - range $=\frac{10.6 + 18.5}{2}=14.55$

Step5: Analyze the shape of the distribution

The mean is $14.375$ and the median is $14.2$. Since the mean is greater than the median, the distribution will probably be skewed to the right.

Answer:

Part 1: $14.375$
Part 2: $14.2$
Part 3: $14$
Part 4: $14.55$
Part 5: The distribution will probably be skewed to the right.