Math / Data & Statistics

QuestionThe table gives information about the times taken by 80 people to run a race.
Time taken ( $t$ minutes) Cumulative Frequency $\begin{array}{ll} 50<t \leq 60 & 15 \\ 50<t \leq 70 & 31 \\ 50<t \leq 80 & 52 \\ 50<t \leq 90 & 66 \\ 50<t \leq 100 & 74 \\ 50<t \leq 110 & 80 \end{array}$
This information is shown on the cumulative frequency graph below.
Use this graph to find an estimate for the interquartile range of the times taken.

Studdy Solution

STEP 1

What is this asking? We need to find the difference between the time it took the person at the 75% mark and the 25% mark to finish the race, using the graph. Watch out! Don't mix up the median and the quartiles!
And be precise when reading values from the graph!

STEP 2

1. Find the Upper Quartile
2. Find the Lower Quartile
3. Calculate the Interquartile Range

STEP 3

The upper quartile represents the time taken by the runner at the 75% mark.
Since there are 80 runners, we need to find the position of the 75% runner.
We calculate this by multiplying $0.75 \cdot 80 = 60$ .

STEP 4

So, the upper quartile is the time taken by the 60th runner.
Locate 60 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

STEP 5

The upper quartile appears to be approximately 87 minutes, based on where our vertical line intersects the time axis.

STEP 6

The lower quartile represents the time taken by the runner at the 25% mark.
We calculate the position of the lower quartile with $0.25 \cdot 80 = 20$ .

STEP 7

So, the lower quartile is the time taken by the 20th runner.
Locate 20 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

STEP 8

The lower quartile appears to be approximately 67 minutes.

STEP 9

The interquartile range is the difference between the upper and lower quartiles.
So, we subtract the lower quartile time from the upper quartile time: $87 - 67 = 20$ .

STEP 10

The interquartile range is approximately 20 minutes.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference between the time it took the person at the 75% mark and the 25% mark to finish the race, using the graph. Watch out! Don't mix up the median and the quartiles!
And be precise when reading values from the graph!

STEP 2

1. Find the Upper Quartile
2. Find the Lower Quartile
3. Calculate the Interquartile Range

STEP 3

The upper quartile represents the time taken by the runner at the 75% mark.
Since there are 80 runners, we need to find the position of the 75% runner.
We calculate this by multiplying $0.75 \cdot 80 = 60$ .

STEP 4

So, the upper quartile is the time taken by the 60th runner.
Locate 60 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

STEP 5

The upper quartile appears to be approximately 87 minutes, based on where our vertical line intersects the time axis.

STEP 6

The lower quartile represents the time taken by the runner at the 25% mark.
We calculate the position of the lower quartile with $0.25 \cdot 80 = 20$ .

STEP 7

So, the lower quartile is the time taken by the 20th runner.
Locate 20 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

STEP 8

The lower quartile appears to be approximately 67 minutes.

STEP 9

The interquartile range is the difference between the upper and lower quartiles.
So, we subtract the lower quartile time from the upper quartile time: $87 - 67 = 20$ .

STEP 10

The interquartile range is approximately 20 minutes.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference between the time it took the person at the 75% mark and the 25% mark to finish the race, using the graph. Watch out! Don't mix up the median and the quartiles!And be precise when reading values from the graph!

STEP 2

1. Find the Upper Quartile2. Find the Lower Quartile3. Calculate the Interquartile Range

STEP 3

The upper quartile represents the time taken by the runner at the **75%** mark.Since there are **80** runners, we need to find the position of the 75% runner.We calculate this by multiplying 0.75⋅80=600.75 \cdot 80 = 600.75⋅80=60.

STEP 4

So, the upper quartile is the time taken by the **60th** runner.Locate **60** on the vertical *cumulative frequency* axis.Draw a horizontal line across to the curve, and then a vertical line down to the *time* axis.

STEP 5

The upper quartile appears to be approximately **87** minutes, based on where our vertical line intersects the time axis.

STEP 6

The lower quartile represents the time taken by the runner at the **25%** mark.We calculate the position of the lower quartile with 0.25⋅80=200.25 \cdot 80 = 200.25⋅80=20.

STEP 7

So, the lower quartile is the time taken by the **20th** runner.Locate **20** on the vertical *cumulative frequency* axis.Draw a horizontal line across to the curve, and then a vertical line down to the *time* axis.

STEP 8

The lower quartile appears to be approximately **67** minutes.

STEP 9

The interquartile range is the difference between the upper and lower quartiles.So, we subtract the lower quartile time from the upper quartile time: 87−67=2087 - 67 = 2087−67=20.

STEP 10

The interquartile range is approximately **20** minutes.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the difference between the time it took the person at the 75% mark and the 25% mark to finish the race, using the graph. Watch out! Don't mix up the median and the quartiles!
And be precise when reading values from the graph!

1. Find the Upper Quartile
2. Find the Lower Quartile
3. Calculate the Interquartile Range

The upper quartile represents the time taken by the runner at the 75% mark.
Since there are 80 runners, we need to find the position of the 75% runner.
We calculate this by multiplying $0.75 \cdot 80 = 60$ .

So, the upper quartile is the time taken by the 60th runner.
Locate 60 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

The upper quartile appears to be approximately 87 minutes, based on where our vertical line intersects the time axis.

The lower quartile represents the time taken by the runner at the 25% mark.
We calculate the position of the lower quartile with $0.25 \cdot 80 = 20$ .

So, the lower quartile is the time taken by the 20th runner.
Locate 20 on the vertical cumulative frequency axis.
Draw a horizontal line across to the curve, and then a vertical line down to the time axis.

The lower quartile appears to be approximately 67 minutes.

The interquartile range is the difference between the upper and lower quartiles.
So, we subtract the lower quartile time from the upper quartile time: $87 - 67 = 20$ .

The interquartile range is approximately 20 minutes.