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Artemon [7]
3 years ago
11

The percentage of cotton in material used to manufacture men's shirts follows.

Mathematics
1 answer:
velikii [3]3 years ago
8 0

Answer:

Median = 34.55

Quartiles:

Q1 = 33.1

Q2 = 34.55

Q3 = 35.6

Inter Quartile range = 2.5

Step-by-step explanation:

Step 1

We arrange the given the following data from lowest to the highest

32.0, 32.1, 32.1, 32.2, 32.4, 32.5, 32.5, 32.5, 32.8, 32.8, 32.8, 32.8, 32.9, 32.9, 33.0, 33.0, 33.2, 33.2, 33.2, 33.2, 33.5, 33.6, 33.8, 33.8, 33.9, 34.0, 34.0, 34.1, 34.1, 34.3, 34.4, 34.5, 34.6, 34.6, 34.6, 34.7, 34.7, 35.0, 35.0, 35.1, 35.1, 35.2, 35.4, 35.5, 35.5, 35.5, 35.5, 35.6, 35.6, 36.1, 36.3, 36.4, 36.4, 36.4, 36.5, 36.6, 36.7, 36.7, 37.0, 37.1, 37.4, 37.4, 37.6, 37.8

a. Construct a stem-and-leaf display for the data.

Stem and leaf Display

Stem | Leaf

32 | 0,1,1,2,4,5,5,5,8,8,8,8,9,9

33 | 0,0,2,2,2,2,5,6,8,8,9

34 | 0,0,1,1,3,4,5,6,6,6,7,7

35 | 0,0,1,1,2,4,5,5,5,5,6,6,

36 | 1,3,4,4,4,5,6,7,7,

37 | 0,1,4,4,6,8

b. Calculate the median and quartiles of these data.

Number of terms = 64

1) Median = 1/2(n + 1)th value

n = 64

= 1/2(64 + 1)th

= 1/2(65)th

= 32.5 th value

This means it is between the 32nd and 33rd value

32nd = 34.5

33rd = 34.6

= 34.5 + 34.6/2

= 69.1/2

= 34.55

2) First Quartile

1/4(n + 1)th value

n = 64

= 1/4(64 + 1)th

= 1/4(65)th

= 16.5th value

This means it is between the 16th and 17th value

16th value = 33.0

17tj value = 33.2

= 33.0 + 33.2/2

= 66.2/2

= 34.55

Q1 --> 33.1

3)Second Quartile = Median

1/2(n + 1)th value

n = 64

= 1/2(64 + 1)th

= 1/2(65)th

= 32.5 th value

This means it is between the 32nd and 33rd value

32nd = 34.5

33rd = 34.6

= 34.5 + 34.6/2

= 69.1/2

= 34.55

Q2 --> 34.55

Third Quartile

3/4(n + 1)th value

n = 64

= 3/4(64 + 1)th

= 3/4(65)th

= 48.75 th value

This means it is towards the 49th value

32nd = 34.5

Hence,

Q3 --> 35.6

Inter Quartile range

Q3 - Q1

= 35.6 - 33.1

= 2.5

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Answer:

The numbers are 23 and 7  

Step-by-step explanation:

1. Set up the equations

   Let x = the greater number

  and y = the smaller number. Then

(1) x - y = 16

       4y = 4 times the smaller number and

  4y - 5 = 5 less than 4 times the smaller number. Then

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You have a system of two equations:

\begin{cases}(1) & x - y = 16\\(2) & x = 4y - 5\end{cases}

2. Solve the equations

\begin{array}{lrcll}(3) & 4y - 5 - y & = & 16 &\text{Substituted (2) into (1)}\\& 3y - 5 & = & 16 &\text{Simplified}\\ & 3y & = & 21 &\text{Added 5 to each side}\\(4) &y & = & \mathbf{7} &\text{Divided each side by 3} \\& x - 7 & = & 16 & \text{Substituted (4) into (1)}\\& x& = & \mathbf{23} & \text{Added 7 to each side}\\\end{array}

The larger number is 23; the smaller number is 7.

3. Check

\begin{array}{rclcrcl}23 - 7& = & 16 & \qquad &23&=&4(7) - 5\\16 & = & 16 & \qquad &23& = &28 - 5\\&&& \qquad &23& = &23\\\end{array}

OK.

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