Math / Data & Statistics

QuestionHere is the five-number summary for the distribution of a cigarette tax (in cents) for all the states in a certain country Use this information to answer parts a through d. $\text { Minimum }=8, \text { Q1 }=37, \text { Median }=52, \text { Q3 }=97, \text { Maximum }=163$ a. About what proportion of the states have cigarette taxes (i) greater than 37 cents and (ii) greater than 97 cents? (i) About $\square$ $\%$ of the states have cigarette taxes greater than 37 cents

Studdy Solution

STEP 1

1. The five-number summary provides key percentiles of the data distribution.
2. $Q1$ (first quartile) represents the 25th percentile.
3. $Q3$ (third quartile) represents the 75th percentile.
4. The median represents the 50th percentile.

STEP 2

1. Determine the proportion of states with taxes greater than 37 cents.
2. Determine the proportion of states with taxes greater than 97 cents.

STEP 3

Understand that $Q1 = 37$ represents the 25th percentile. This means 25% of the states have cigarette taxes less than or equal to 37 cents.

STEP 4

Calculate the proportion of states with taxes greater than 37 cents. Since 25% have taxes less than or equal to 37 cents, the remaining proportion is:
$100\% - 25\% = 75\%$

STEP 5

Understand that $Q3 = 97$ represents the 75th percentile. This means 75% of the states have cigarette taxes less than or equal to 97 cents.

STEP 6

Calculate the proportion of states with taxes greater than 97 cents. Since 75% have taxes less than or equal to 97 cents, the remaining proportion is:
$100\% - 75\% = 25\%$
The answers are: (i) About $75\%$ of the states have cigarette taxes greater than 37 cents. (ii) About $25\%$ of the states have cigarette taxes greater than 97 cents.

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Studdy Solution

STEP 1

1. The five-number summary provides key percentiles of the data distribution.
2. $Q1$ (first quartile) represents the 25th percentile.
3. $Q3$ (third quartile) represents the 75th percentile.
4. The median represents the 50th percentile.

STEP 2

1. Determine the proportion of states with taxes greater than 37 cents.
2. Determine the proportion of states with taxes greater than 97 cents.

STEP 3

Understand that $Q1 = 37$ represents the 25th percentile. This means 25% of the states have cigarette taxes less than or equal to 37 cents.

STEP 4

Calculate the proportion of states with taxes greater than 37 cents. Since 25% have taxes less than or equal to 37 cents, the remaining proportion is:
$100\% - 25\% = 75\%$

STEP 5

Understand that $Q3 = 97$ represents the 75th percentile. This means 75% of the states have cigarette taxes less than or equal to 97 cents.

STEP 6

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Studdy Solution

STEP 1

1. The five-number summary provides key percentiles of the data distribution.2. Q1 Q1 Q1 (first quartile) represents the 25th percentile.3. Q3 Q3 Q3 (third quartile) represents the 75th percentile.4. The median represents the 50th percentile.

STEP 2

1. Determine the proportion of states with taxes greater than 37 cents.2. Determine the proportion of states with taxes greater than 97 cents.

STEP 3

Understand that Q1=37 Q1 = 37 Q1=37 represents the 25th percentile. This means 25% of the states have cigarette taxes less than or equal to 37 cents.

STEP 4

Calculate the proportion of states with taxes greater than 37 cents. Since 25% have taxes less than or equal to 37 cents, the remaining proportion is:100%−25%=75% 100\% - 25\% = 75\% 100%−25%=75%

STEP 5

Understand that Q3=97 Q3 = 97 Q3=97 represents the 75th percentile. This means 75% of the states have cigarette taxes less than or equal to 97 cents.

STEP 6

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.

1. The five-number summary provides key percentiles of the data distribution.
2. $Q1$ (first quartile) represents the 25th percentile.
3. $Q3$ (third quartile) represents the 75th percentile.
4. The median represents the 50th percentile.

1. Determine the proportion of states with taxes greater than 37 cents.
2. Determine the proportion of states with taxes greater than 97 cents.

Understand that $Q1 = 37$ represents the 25th percentile. This means 25% of the states have cigarette taxes less than or equal to 37 cents.

Calculate the proportion of states with taxes greater than 37 cents. Since 25% have taxes less than or equal to 37 cents, the remaining proportion is:
$100\% - 25\% = 75\%$

Understand that $Q3 = 97$ represents the 75th percentile. This means 75% of the states have cigarette taxes less than or equal to 97 cents.