Question

consider the following data set.
79.7 45.9 71.5 64.1 66.9 78.1 63.8 50.5 53.1 62.2
find the following:
mean =
median =
mode =

• if there is no mode, type dne.
• if there is more than one mode, type them all separated by commas.

range =

Explanation:

Step1: Calculate the mean

First, sum all the data points: \(79.7 + 45.9 + 71.5 + 64.1 + 66.9 + 78.1 + 63.8 + 50.5 + 53.1 + 62.2\). Let's compute that: \(79.7+45.9 = 125.6\); \(125.6 + 71.5 = 197.1\); \(197.1+64.1 = 261.2\); \(261.2+66.9 = 328.1\); \(328.1+78.1 = 406.2\); \(406.2+63.8 = 470\); \(470+50.5 = 520.5\); \(520.5+53.1 = 573.6\); \(573.6+62.2 = 635.8\). There are 10 data points, so the mean is \(\frac{635.8}{10}=63.58\).

Step2: Find the median

First, sort the data set in ascending order: \(45.9, 50.5, 53.1, 62.2, 63.8, 64.1, 66.9, 71.5, 78.1, 79.7\). Since there are 10 (even) data points, the median is the average of the 5th and 6th values. The 5th value is \(63.8\) and the 6th is \(64.1\). So median is \(\frac{63.8 + 64.1}{2}=\frac{127.9}{2}=63.95\).

Step3: Determine the mode

A mode is a value that appears most frequently. In this data set, all values appear only once, so there is no mode (DNE).

Step4: Calculate the range

Range is the maximum value minus the minimum value. The maximum value is \(79.7\) and the minimum is \(45.9\). So range is \(79.7 - 45.9 = 33.8\).

Answer:

mean = \(63.58\)
median = \(63.95\)
mode = DNE
range = \(33.8\)