Question

1. dr jordan volunteers with a local environmental group studying lakes in franklin county. yesterday, she measured and recorded the water temperatures in the nearby lakes. 75 73 65 69 71 73 68 74 mean = ____ median = __ mode = __ range = __ shape: ____

Explanation:

Step1: Calculate the mean

The mean is the sum of all values divided by the number of values. The sum of the temperatures \(75 + 73+65 + 69+71+73+68+74=568\), and there are \(n = 8\) values. So the mean \(\bar{x}=\frac{568}{8}=71\).

Step2: Calculate the median

First, order the data: \(65,68,69,71,73,73,74,75\). Since \(n = 8\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The 4th value is \(71\) and the 5th value is \(73\), so the median \(M=\frac{71 + 73}{2}=72\).

Step3: Calculate the mode

The mode is the value that appears most frequently. The number \(73\) appears twice, and all other numbers appear once, so the mode is \(73\).

Step4: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value is \(75\) and the minimum value is \(65\), so the range \(R=75 - 65 = 10\).

Step5: Determine the shape

From the histogram (right - skewed as the tail is on the right side), the data is right - skewed. The mean (\(71\)) is less than the median (\(72\)) which is also an indication of right - skewness.

Answer:

Mean = \(71\)
Median = \(72\)
Mode = \(73\)
Range = \(10\)
Shape: Right - skewed