Ivanna spent a total of

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

2 years ago

A cylinder shaped container has a radius of 30 cm and a height of 100 cm. A glass sphere with a redius of 12 cm is placed inside

Artemon [7]

Vcylinder-Vsphere=water

Vcylinder=hpir^2
Vsphere=(4/3)pir^3

given

cylinderradius=30 and h=100
Vcylinder=100pi30^2=100pi900=90000pi
let's leave it in terms of pi for more exactness

sphereradius=12
Vsphere=(4/3)pi12^3=2304pi

cylinder-sphere=90000pi-2304pi=87696pi
using pi=3.14
water=275365.44 cubic cm

last option is corrrect

4 0

3 years ago

If you know the volume of a cylinder and that a cone has the same base and height of a cone, how would you determine the volume

ratelena [41]

Answer:

Multiply the cone's volume by 3

Step-by-step explanation:

Cylinder's Volume is

V = pi r ^2(h)

Cone's Volume is

V = 1/3 pi r^2 (h)

5 0

3 years ago

Read 2 more answers

I want to know how to get this factored and simplified the easiest way. I know that I can multiply out and then factor but that

Reptile [31]

Answer:

Enter the expression you want to factor in the editor. The Factoring Calculator transforms complex expressions into a product of simpler factors. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions.

Step-by-step explanation:

8 0

2 years ago

(11-5) + 6) + 13 - 42<br> Pls help I’ll mark brainliest

g100num [7]

Answer:

-17

Step-by-step explanation:

4 0

3 years ago