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dusya [7]
3 years ago
9

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

Mathematics
1 answer:
poizon [28]3 years ago
8 0

Answer:

Mean: \bar x = 40.61

Median =40.2

Mode = 43.4

Step-by-step explanation:

Given

See attachment for data

Solving (a): The mean

Mean is calculated as:

\bar x = \frac{\sum x}{n}

From the attached:

n = 14

So, the mean is:

\bar x = \frac{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 = \frac{568.58}{14}

\bar x = 40.61

Solving (b): The median

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

Median = \frac{1}{2}(n+1)

Median = \frac{1}{2}(14+1)

Median = \frac{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): <em>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.</em>

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

The median is:

Median = \frac{1}{2}(40.2 + 40.2)

Median = \frac{1}{2}*80.4

Median =40.2

Solving (c): The mode

43.4 has the highest number of occurrence.

So:

Mode = 43.4

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The amount of substance left of a radioactive element of half life, t_{\frac{1}{2}} after a time, t, is given by:

N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{  \frac{1}{2} }}

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The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:

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