Questions: Lengths of a random sample of 6 rivers on the South island of New Zealand that flow to the Tasman Sea measured in kilometers are listed in the table below. Length 51 48 37 56 35 64 For the data shown above, find the following. Round answer in the first blank to 1 decimal place(s). In the second blank put the correct units. Find the mean: Select an answer Find the median: Select an answer Find the range: Select an answer Find the variance: Select an answer Find the standard deviation: Select an answer

Solution Steps

To solve the given problem, we need to calculate the mean, median, and range of the lengths of the rivers. Here is the approach:

1. Mean: Sum all the lengths and divide by the number of lengths.
2. Median: Sort the lengths and find the middle value. If there is an even number of lengths, take the average of the two middle values.
3. Range: Subtract the smallest length from the largest length.

The mean of a set of numbers is given by the sum of the numbers divided by the count of the numbers. For the given lengths of rivers:

\[ \text{Mean} = \frac{51 + 48 + 37 + 56 + 35 + 64}{6} = \frac{291}{6} = 48.5 \text{ km} \]

The median is the middle value of a sorted list of numbers. If the list has an even number of elements, the median is the average of the two middle numbers. For the given lengths, when sorted:

\[ [35, 37, 48, 51, 56, 64] \]

Since there are 6 numbers, the median is the average of the 3rd and 4th numbers:

\[ \text{Median} = \frac{48 + 51}{2} = \frac{99}{2} = 49.5 \text{ km} \]

The range of a set of numbers is the difference between the largest and smallest numbers. For the given lengths:

\[ \text{Range} = 64 - 35 = 29 \text{ km} \]

Final Answer