1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveta [45]
2 years ago
13

Teacher raises A school system employs teachers at

Mathematics
1 answer:
Cerrena [4.2K]2 years ago
6 0

By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) <u>The shape of the data remains the same</u>

(b) <u>The mean and median are increased by $1,000</u>

(c) <u>The standard deviation and interquartile range remain the same</u>

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

\overline x = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i}

Therefore, following an increase of $1,000, we have;

 \overline x_{New} = \dfrac{\sum (f_i \cdot (x_i + 1000))}{\sum f_i} =  \dfrac{\sum (f_i \cdot x_i + f_i \cdot 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i}

\overline x_{New} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + 1000 = \overline x + 1000

  • Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, x_i, are increased by $1,000, the median salary, x_{med}, is also increased by $1,000

Therefore;

  • The correct response is that the median is increased by $1,000

(c) The standard deviation, σ, is given by \sigma =\sqrt{\dfrac{\sum \left (x_i-\overline x  \right )^{2} }{n}};

Where;

n = The number of teaches;

Given that, we have both a salary, x_i, and the mean, \overline x, increased by $1,000, we can write;

\sigma_{new} =\sqrt{\dfrac{\sum \left ((x_i + 1000) -(\overline x  + 1000)\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x  - 1000\right )^{2} }{n}}

\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x  - 1000\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}}

\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}} =\sqrt{\dfrac{\sum \left (x_i-\overline x  \right )^{2} }{n}} = \sigma

Therefore;

\sigma_{new} = \sigma; <u>The standard deviation stays the same</u>

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR_{new} = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

  • <u>The interquartile range stays the same</u>

Learn more here:

brainly.com/question/9995782

You might be interested in
A lake contain 900 gallons of water. The city is pumping water into the lake at a rate of 30 gallons per minute. Which expressio
boyakko [2]

Answer:

900 + 12 x 30

Step-by-step explanation:

4 0
2 years ago
What is the midpoint between (3,5) and (7,9)
NikAS [45]
Your anbswer is gonna be 5,7
5 0
3 years ago
Read 2 more answers
Help please!!!!! What is the answer (algebra)
zaharov [31]

Answer:

girlllllllll let me work it out lol

Step-by-step explanation:

8 0
3 years ago
THe temperature is negative 7 degrees and overnight it gets 12 degrees warmer? Then during the day it gets 12 degrees warmer?
Vinil7 [7]
At the start the temperature is -7 overnight it gets 12 degrees warmer so -7+12 =5 degrees than during the day it gets 12 degrees warmer so 5+12= 17 degrees
6 0
2 years ago
Can somebody please help me with these two questions?
vovikov84 [41]
The answer to 25. is A
and 
to 26. is C (I'm not sure on this one but i think this is the answer)
6 0
3 years ago
Read 2 more answers
Other questions:
  • Alicia is going to the animal shelter to adopt a new pet. If there are 15 cats, 24 dogs and 3 horses, what is the probability sh
    14·2 answers
  • 60% expressed as a ration is 60 Over 100 . What is this as a fraction in its reduced form?
    11·1 answer
  • PLEASE help and explain hoot do this. I need help with 4,5,6
    15·1 answer
  • It has a length of 3 ft and a height of 1.4 ft. What is the width of the sink?
    11·1 answer
  • Find two consecutive whole numbers that 58 lies between?
    12·2 answers
  • the regular price of a shirt is $15 natalie bought it on a sale for 0.9 times then the sale price was multiplied by 1.06 to incl
    15·1 answer
  • Simplify each expression by distributing and combining like terms <br> 6(x + 1) – 5(x + 2)
    7·2 answers
  • A runner’s distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. O
    11·1 answer
  • A survey Was contacted to determine the favorite snack food at 300 shoppers at a grocery store. The circle graph shows the resul
    10·1 answer
  • Find x pls help me this is due soon
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!