Question

• 1) For what data in your professional or personal life would it be useful to construct a frequency table or histogram? If you give this some thought, you should be able to identify several sets of data.

  2) After using the formula for determining the value of P₁₆ (the 16th percentile) in a data set, the result is L = 5 (this whole number was obtained without rounding). How do we use this result to determine the value of P₁₆?

  3) It is common for car insurance companies to charge higher premiums for younger drivers. Younger drivers tend to earn less income than older drivers on average. So why are younger drivers expected to pay higher premiums? Do insurance companies have a right to charge different premiums to different customers for the same coverage based on their age?

Answer 1

1)

a) This histogram for representing the number of students scoring a certain grades(A,B,C,D,E,F) of from the last geometry test.

b) number of employees in each pay-grade (50k-60k,60k-70k...100k-110k)

2) To calculate the k^th percentile (where k is any number between zero and one hundred), do the following steps:

1. Order all the values in the data set from smallest to largest.

2. Multiply k percent by the total number of values, n.

   This number is called the index.

3. If the index obtained in Step 2 is not a whole number, round it up to the nearest whole number and go to Step 4a. If the index obtained in Step 2 is a whole number, go to Step 4b.

4. 4a.Count the values in your data set from left to right (from the smallest to the largest value) until you reach the number indicated by Step 3.

   The corresponding value in your data set is the k^th percentile.

5. 4b.Count the values in your data set from left to right until you reach the number indicated by Step 2.

   The k^th percentile is the average of that corresponding value in your data set and the value that directly follows it.

For example, suppose you have 25 test scores, and in order from lowest to highest they look like this: 43, 54, 56, 61, 62, 66, 68, 69, 69, 70, 71, 72, 77, 78, 79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99. To find the 90th percentile for these (ordered) scores, start by multiplying 90% times the total number of scores, which gives 90% ? 25 = 0.90 ? 25 = 22.5 (the index). Rounding up to the nearest whole number, you get 23.

Counting from left to right (from the smallest to the largest value in the data set), you go until you find the 23rd value in the data set. That value is 98, and it’s the 90th percentile for this data set.

Now you want to find the 16th percentile. Start by taking 0.16 * X = 5 =>x=32.5;(the index=5) this is a whole number, so proceed from Step 3 to Step 4b, which tells you the 16th percentile is the average of the 5th and 6th values in the ordered data set.The 16th percentile then comes to (5th + 6th) ÷ 2

3)It is common for car insurance companies to charge higher premiums for younger drivers. Younger drivers tend to earn less income than older drivers on average. younger drivers expected to pay higher premiums, may be because of the fact that younger driver are often less experienced in driving than the older drivers,Statistically, young men are riskier drivers, which means they are, on average, more expensive to insure.hence young drivers have higher change of accidents / insurance claim compared to older ones.

yes insurance companies do have a right to charge different premiums to different customers for the same coverage based on their age and it is a common practice.