Recently, a random sample of 13-18 year olds was asked, "How much do you currently have in savings?" The data in the table re
present the responses to the survey. Approximate the mean and standard deviation amount of savings.
1 answer:
Answer:
μ = 235.38
σ = 234.54
Step-by-step explanation:
Assuming the table is as follows:
This is an example of grouped data, where a range of values is given rather than a single data point. First, find the total frequency.
n = 339 + 86 + 55 + 18 + 11 + 8 + 3
n = 520
The mean is the expected value using the midpoints of each range.
μ = (339×100 + 86×300 + 55×500 + 18×700 + 11×900 + 8×1100 + 3×1300) / 520
μ = 122400 / 520
μ = 235.38
The variance is:
σ² = [(339×100² + 86×300² + 55×500² + 18×700² + 11×900² + 8×1100² + 3×1300²) − (520×235.38²)] / (520 − 1)
σ² = 55009.7
The standard deviation is:
σ = 234.54
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Answer:
3x + y = 20 and x - 2y = - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
Given
3x + y = 17 ( subtract 3x from both sides )
y = - 3x + 17 ← in slope- intercept form
with slope m = - 3
Para;;el lines have equal slopes , then
y = - 3x + c ← is the partial equation
To find c substitute (4, 8) into the partial equation
8 = - 12 + c ⇒ c = 8 + 12 = 20
y = - 3x + 20 ← in slope- intercept form
Add 3x to both sides
3x + y = 20 ← in standard form
--------------------------------------------------------
(b)
Given
y + 2x = 13 ( subtract 2x from both sides )
y = - 2x + 13 ← in slope- intercept form
with slope m = - 2
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
=
, then
y = x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 1 + c ⇒ c = 3 - 1 = 2
y = x + 2 ← in slope- intercept form
Multiply through by 2 to clear the fraction
2y = x + 4
x - 2y = - 4 ← in standard form