Question

Calculate Decile 8 of the following sample: 10 11 12 13 14 15 16 18 18 19 20 20 22 23 25 26 27 28 29 30

176

likes
881 views

Answer to a math question Calculate Decile 8 of the following sample: 10 11 12 13 14 15 16 18 18 19 20 20 22 23 25 26 27 28 29 30

Expert avatar
Darrell
4.5
100 Answers
Solution:
1. Given sample data:
* 10, 11, 12, 13, 14, 15, 16, 18, 18, 19, 20, 20, 22, 23, 25, 26, 27, 28, 29, 30

2. Order the data set (already ordered):
* 10, 11, 12, 13, 14, 15, 16, 18, 18, 19, 20, 20, 22, 23, 25, 26, 27, 28, 29, 30

3. To find the position of the 8th decile (D8), use the formula:
D_k = \left( \frac{k(n + 1)}{10} \right)^{th} \text{ position}
where k = 8 and n = 20 (number of data points).

4. Calculate the position:
D_8 = \left( \frac{8(20 + 1)}{10} \right) = \left( \frac{168}{10} \right) = 16.8^{th} \text{ position}

5. Since 16.8 isn't a whole number, it means D8 is between the 16th and 17th data points. Using interpolation:
- 16th value is 26 and 17th value is 27.
- Interpolating:
D_8 = 26 + 0.8(27 - 26)
D_8 = 26 + 0.8(1)
D_8 = 26.8

6. Therefore, the 8th decile (D8) is:
26.8

Frequently asked questions (FAQs)
Find the value of x such that the logarithmic function f(x) = log(x) equals the natural logarithmic function g(x) = ln(x).
+
Math Question: Graph the inequality y ≤ 2x + 3 on a coordinate plane. (
+
What is the length of the side opposite the angle θ in a right-angled triangle, given the adjacent side length and angle θ?
+
New questions in Mathematics
The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?
5(4x+3)=75
The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .
2x-4y=-6; -4y+4y=-8
The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =
-0.15/32.6
-3(-4x+5)=-6(7x-8)+9-10x
Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)
Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25
Express the trigonometric form of the complex z = -1 + i.
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
Find the area of a triangle ABC when m<C = 14 degrees, a = 5.7 miles, and b = 9.3 miles.
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
if y=1/w^2 yw=2-x; find dy/dx
2+2020202
Solve the following 9x - 9 - 6x = 5 + 8x - 9
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart
23,456 + 3,451