Question

One of the events in the Winter Olympics is the Men's 500-meter Speed Skating.

The times for this event are shown below.

Find the mean,mode,and median time

Answer 1

Mean:
`\bar x = 40.61`

`Median =40.2`

`Mode = 43.4`

Explanation:

Given

See attachment for data

Solving (a): The mean

Mean is calculated as:

`\bar x = (\sum x)/(n)`

From the attached:

`n = 14`

So, the mean is:

`\bar x = (43.4+43.4+43.4+43.1+43.2+40.2+40.2+40.1+40.3+39.44+39.17+38.03+38.19+36.45)/(14)`

`\bar x = (568.58)/(14)`

`\bar x = 40.61`

Solving (b): The median

`n = 14`; this is an even number. So, the median is:

`Median = (1)/(2)(n+1)`

`Median = (1)/(2)(14+1)`

`Median = (1)/(2)(15)`

`Median = 7.5th`

This implies that the median is the average of the 7th and 8th item.

Next, is to order the data (in ascending order): 36.45, 38.03, 38.19, 39.17, 39.44, 40.1, 40.2, 40.2, 40.3, 43.1, 43.2, 43.4, 43.4, 43.4.

The 7th and 8th items are: 40.2 and 40.2

The median is:

`Median = (1)/(2)(40.2 + 40.2)`

`Median = (1)/(2)*80.4`

`Median =40.2`

Solving (c): The mode

43.4 has the highest number of occurrence.

So:

`Mode = 43.4`